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Dr. Raven Henderson founded Dynobite Smiles in 2008 with a mission of "Treating little smiles in a big way." Dr. Henderson graduated from Howard University with her DDS and certificate in pediatric dentistry. She enjoys teaching the pediatric dental residents at Yale and spending time with her son, Luke and husband, Marc.


It is exceedingly difficult to measure the quality of one's life. The reason for this difficulty is the fact that life is unpredictable. One day may be horrible and the next day may be amazing. Does this make the average quality of one's life mediocre? The answer to this question may be, "Absolutely!" to some people and, "No way," to others. Given that each individual places different criteria on determining the quality of life it becomes horrendously difficult to measure.
If you are going to attempt to measure the quality of life it is essential the criteria and definitions for that set of criteria be established. For example, physical and emotional pain may lessen the quality of one's life, but a scale would need to be developed to determine how much weight that has in the determination of the quality of life. Additionally, physical and emotional pleasure and joy may increase the quality of one's life, but a scale to measure these aspects of life would also need to be established.
Once criteria have been set and a means in which to measure that set of criteria has been established the next step is to record the goings-on of one's life for several days. Everything that increases or decreases the quality of one's life according to the previous defined criteria should be recorded. At the end of the recording period you can determine where the quality of the life is based upon your measurement standards.
Though a means in which to measure quality of life has been outlined, it is important to remember that each individual is going to have vastly different criteria from other individuals. This simply goes to show that people are different and have very different needs, wants, and desires. It is important to remember that just because someone may not have a very high quality of life to your particular standards does not mean that he or she does not have an astronomically high quality of life to his or her standards. Keep in mind that it is the individual that must cope with his or her life and life circumstances. When measuring the quality of life try to simply keep an eye on your quality of life and do the best that you can to improve it. Try your best not to judge others for the ways that they choose to live because they very well may be quite happy and content.


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The very advanced Nicmos CryoCooler designed to cool Nicmos onboard Hubble.
Astronomers all over the world are already eagerly anticipating the return of Nicmos (Near Infrared Camera and Multi-Object Spectrometer), the sharpest definition infrared instrument in existence, after more than two years of enforced rest.
Nicmos was originally installed onboard Hubble during the second Servicing Mission (SM2) in February 1997. Designed to operate at infrared wavelengths, Nicmos had to be cooled so that its own heat did not interfere with the infrared detectors. In the case of Nicmos, cooling is produced by solid nitrogen at -196 °C, encased in an advanced thermos flask system.
Unfortunately Nicmos' lifetime was reduced from the expected 4.5 years to about 2, due to a problem in the cooling system. The sides of the thermos flask touched and as a result the solid nitrogen inside heated up and evaporated, so that by January 1999 all the coolant nitrogen had disappeared and Nicmos could no longer operate.
Once the problem was recognised the Space Telescope scheduling was adjusted in such a way that Nicmos observations were assigned to as much as 40-50% of the total observing time during the first period of observations after the instrument was installed. In this way the Nicmos science programme was completed despite the instrument's dramatically shortened lifetime.
But at last, after this enforced shutdown, Nicmos has been revived. Astronauts retrofitted it with a new, experimental cooling system that returned it to active duty. By fitting Nicmos with this refrigerator-like cooling system, it is again possible to re-cool the detectors to -196 ºC (77 K), thereby reawakening their infrared vision and extending the instrument's life by several years.
The super-quiet cooler (called the Nicmos CryoCooler - NCC) uses ultra-high-speed microturbines, spinning up to more than 400 000 rpm (revolutions per minute)- over 100 times the revolutions of a typical car engine). Hubble's engineering team successfully demonstrated this technology in 1998 during another Shuttle mission in the first on-orbit test of this high-performance, high-efficiency, mechanical cryocooler.
In the past Nicmos has produced excellent science and astronomers are looking forward to working with this top class instrument again.
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redpajama_set_name: RedPajamaCommonCrawl


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CalculusCalculus (MindTap Course List)5-6 Use the graphs of f and g and their tangent lines at (2, 0) too find lim x → 2 f ( x ) g ( x ) .
5-6 Use the graphs of f and g and their tangent lines at (2, 0) too find lim x → 2 f ( x ) g ( x ) .
6.1 Inverse Functions6.2 Exponential Functions And Their Derivatives6.3 Logarithmic Functions6.4 Derivatives Of Logarithmic Functions6.2Star The Natural Logarithmic Function6.3Star The Natural Exponential Function6.4Star General Logarithmic And Exponential Functions6.5 Exponential Growth And Decay6.6 Inverse Trigonometric Functions6.7 Hyperbolic Functions6.8 Indeterminate Forms And I'hospital's Rule6.R Review6.P Problem Plus
Problem 100E
Chapter 6.8, Problem 6E
Ch. 6.1 - a What is one-to-one function? b How can you tell...Ch. 6.1 - a Suppose f is a one-to-one function with domain A...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...
Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - A function is given by a table of values, a graph,...Ch. 6.1 - Assume that f is a one-to-one function. a If...Ch. 6.1 - If f(x)=x5+x3+x, find f1(3) and f(f1(2)).Ch. 6.1 - If h(x)=x+x, find h1(6).Ch. 6.1 - The graph of f is given. a Why is f one-to-one? b...Ch. 6.1 - The formula C=59(F32), where F459.67, expresses...Ch. 6.1 - In the theory of relativity, the mass of a...Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find a formula for the inverse of the function....Ch. 6.1 - Find an explicit formula for f1 and use it to...Ch. 6.1 - Find an explicit formula for f1 and use it to...Ch. 6.1 - Use the given graph of f to sketch the graph of...Ch. 6.1 - Use the given graph of f to sketch the graph of...Ch. 6.1 - Let f(x)=1x2,0x1. a Find f1. How is it related to...Ch. 6.1 - Let g(x)=1x33. a Find g1. How is it related to g?...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - a Show that f is one-to-one. b Use Theorem 7 to...Ch. 6.1 - Find (f1)(a). f(x)=3x3+4x2+6x+5,a=5Ch. 6.1 - Find (f1)(a). f(x)=x3+3sinx+2cosx,a=2Ch. 6.1 - Find (f1)(a). f(x)=3+x2+tan(x/2),1x1,a=3Ch. 6.1 - Find (f1)(a). f(x)=x3+4x+4,a=3Ch. 6.1 - Suppose f1 is the inverse function of a...Ch. 6.1 - If g is an increasing function such that g(2)=8...Ch. 6.1 - If f(x)=3x1+t3dt, find (f1)(0).Ch. 6.1 - Suppose f1 is the inverse function of a...Ch. 6.1 - Graph the function f(x)=x3+x2+x+1 and explain why...Ch. 6.1 - Show that h(x)=sinx,x, is not one-to-one, but its...Ch. 6.1 - a If we shift a curve to the left, what happens to...Ch. 6.1 - a If f is a one-to-one, twice differentiable...Ch. 6.2 - a Write an equation that defines the exponential...Ch. 6.2 - a How is the number e defined? b What is an...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Graph the given functions on a common screen. How...Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - Make a rough sketch of the graph of the function....Ch. 6.2 - 7-12 Make a rough sketch of the graph of the...Ch. 6.2 - 7-12 Make a rough sketch of the graph of the...Ch. 6.2 - Starting with the graph of y=ex, write the...Ch. 6.2 - Starting with the graph of y=ex, find the equation...Ch. 6.2 - Find the domain of each function. a f(x)=1ex21e1x2...Ch. 6.2 - Find the domain of each function. a g(t)=10t100b...Ch. 6.2 - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.2 - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.2 - Suppose the graphs of f(x)=x2 and g(x)=2x are...Ch. 6.2 - Compare the functions f(x)=x5 and g(x)=5x by...Ch. 6.2 - Compare the functions f(x)=x10 and g(x)=ex by...Ch. 6.2 - Use a graph to estimate the values of x such that...Ch. 6.2 - 23-30 Find the limit. limx(1.001)xCh. 6.2 - 23-30 Find the limit. limx(1.001)xCh. 6.2 - 23-30 Find the limit. limxe3xe3xe3x+e3xCh. 6.2 - 23-30 Find the limit. limxex2Ch. 6.2 - 23-30 Find the limit. limx2+e3/(2x)Ch. 6.2 - 23-30 Find the limit. limx2+e3/(2x)Ch. 6.2 - 23-30 Find the limit. limx(e2xcosx)Ch. 6.2 - 23-30 Find the limit. limx(/2)etanxCh. 6.2 - 31-50 Differentiate the function. f(x)=e5Ch. 6.2 - 31-50 Differentiate the function. k(r)=er+reCh. 6.2 - 31-50 Differentiate the function. f(x)=(3x25x)exCh. 6.2 - 31-50 Differentiate the function. y=ex1exCh. 6.2 - 31-50 Differentiate the function. y=eax3Ch. 6.2 - 31-50 Differentiate the function. g(x)=ex2xCh. 6.2 - 31-50 Differentiate the function. y=etanCh. 6.2 - 31-50 Differentiate the function. V(t)=4+ttetCh. 6.2 - 31-50 Differentiate the function. f(x)=x2exx2+exCh. 6.2 - 31-50 Differentiate the function. y=x2e1/xCh. 6.2 - 31-50 Differentiate the function. y=x2e3xCh. 6.2 - 31-50 Differentiate the function. f(t)=tan(1+e2t)Ch. 6.2 - 31-50 Differentiate the function. f(t)=eatsinbtCh. 6.2 - 31-50 Differentiate the function. f(z)=ez/(z1)Ch. 6.2 - 31-50 Differentiate the function. F(t)=etsin2tCh. 6.2 - 31-50 Differentiate the function....Ch. 6.2 - 31-50 Differentiate the function. g(u)=esecu2Ch. 6.2 - 31-50 Differentiate the function. y=1+xe2xCh. 6.2 - 31-50 Differentiate the function. y=cos(1e2x1+e2x)Ch. 6.2 - 31-50 Differentiate the function....Ch. 6.2 - 51-52 Find an equation of the tangent line to the...Ch. 6.2 - 51-52 Find an equation of the tangent line to the...Ch. 6.2 - Find yifex/y=xy.Ch. 6.2 - Find an equation of the tangent line to the curve...Ch. 6.2 - Show that the function y=ex+ex/2 satisfies the...Ch. 6.2 - Show that the function y=Aex+Bxex satisfies the...Ch. 6.2 - For what values of r does the function y=erx...Ch. 6.2 - Find the values of for which y=ex satisfies the...Ch. 6.2 - If f(x)=e2x, find a formula for f(n)(x).Ch. 6.2 - Find the thousandth derivative of f(x)=xex.Ch. 6.2 - a Use the Intermediate Value Theorem to show that...Ch. 6.2 - Use a graph to find an initial approximation to...Ch. 6.2 - Use the graph of V in Figure 11 to estimate the...Ch. 6.2 - A researcher is trying to determine the doubling...Ch. 6.2 - Under certain circumstances a rumor spreads...Ch. 6.2 - An object is attached to the end of a vibrating...Ch. 6.2 - Find the absolute maximum value of the function...Ch. 6.2 - Find the absolute minimum value of the function...Ch. 6.2 - 69-70 Find the absolute maximum and absolute...Ch. 6.2 - 69-70 Find the absolute maximum and absolute...Ch. 6.2 - 71-72 Find a the intervals of increase or...Ch. 6.2 - 71-72 Find a the intervals of increase or...Ch. 6.2 - 73-75 Discuss the curve using the guidelines of...Ch. 6.2 - 73-75 Discuss the curve using the guidelines of...Ch. 6.2 - 73-75 Discuss the curve using the guidelines of...Ch. 6.2 - Let g(x)=ecx+f(x) and h(x)=ekxf(x), where...Ch. 6.2 - A drug response curve describes the level of...Ch. 6.2 - After an antibiotic tablet is taken, the...Ch. 6.2 - After the consumption of an alcoholic beverage,...Ch. 6.2 - 80-81 Draw a graph of f that shows all the...Ch. 6.2 - 80-81 Draw a graph of f that shows all the...Ch. 6.2 - The family of bell-shaped curves y=12e(x)2/(22)...Ch. 6.2 - 83-94 Evaluate the integral. 01(xe+ex)dxCh. 6.2 - 83-94 Evaluate the integral. 55edxCh. 6.2 - 83-94 Evaluate the integral. 02dxexCh. 6.2 - 83-94 Evaluate the integral. x2ex3dxCh. 6.2 - 83-94 Evaluate the integral. ex1+exdxCh. 6.2 - 83-94 Evaluate the integral. (1+ex)2exdxCh. 6.2 - 83-94 Evaluate the integral. (ex+ex)2dxCh. 6.2 - 83-94 Evaluate the integral. ex(4+ex)5dxCh. 6.2 - 83-94 Evaluate the integral. eu(1eu)2duCh. 6.2 - 83-94 Evaluate the integral. esincosdCh. 6.2 - 83-94 Evaluate the integral. 12e1/xx2dxCh. 6.2 - 83-94 Evaluate the integral. 011+exexdxCh. 6.2 - Find, correct to three decimal places, the area of...Ch. 6.2 - Find f(x) if f(x)=3ex+5sinx,f(0)=1, and f(0)=2.Ch. 6.2 - Find the volume of the solid obtained by rotating...Ch. 6.2 - Find the volume of the solid obtained by rotating...Ch. 6.2 - The error function erf(x)=20xet2dt Is used in...Ch. 6.2 - Show that the function y=ex2erf(x) Satisfies the...Ch. 6.2 - An oil storage tank ruptures at time t=0 and oil...Ch. 6.2 - A bacteria population starts with 400 bacteria and...Ch. 6.2 - Dialysis treatment removes urea and other waste...Ch. 6.2 - The rate of growth of a fish population was...Ch. 6.2 - If f(x)=3+x+ex, find (f1)(4).Ch. 6.2 - Evaluate limxesinx1x.Ch. 6.2 - If you graph the function f(x)=1e1/x1+e1/x Youll...Ch. 6.2 - Graph several members of the family of functions...Ch. 6.2 - a Show that ex1+x if x0. Hint: Show that...Ch. 6.2 - a Use the inequality of Exercise 109a to show...Ch. 6.2 - a Use mathematical induction to prove that for x0...Ch. 6.3 - a How is logarithmic function y=logbx defined? b...Ch. 6.3 - a What is the natural logarithm? b What is the...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - 3-8 Find the exact value of each expression. a...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - Use the properties of logarithms to expand the...Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - 13-18 Express the quantity as a single logarithm....Ch. 6.3 - Use formula 7 to evaluate each logarithm correct...Ch. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - 20-22 Use formula 7 to graph the given functions...Ch. 6.3 - Make a rough sketch of the graph of each function....Ch. 6.3 - 23-24 Make a rough sketch of the graph of each...Ch. 6.3 - 25-26 a What are the domain and range of f? b What...Ch. 6.3 - 25-26 a What are the domain and range of f? b What...Ch. 6.3 - 27-36 Solve each equation for x a e74x=6 b...Ch. 6.3 - 27-36 Solve each equation for x a ln(x21)=3 b...Ch. 6.3 - 27-36 Solve each equation for x a 2x5=3 b...Ch. 6.3 - 27-36 Solve each equation for x a e3x+1=k b...Ch. 6.3 - 27-36 Solve each equation for x ee2x=1Ch. 6.3 - 27-36 Solve each equation for x 10(1+ex)1=3Ch. 6.3 - 27-36 Solve each equation for x ln(lnx)=1Ch. 6.3 - 27-36 Solve each equation for x eex=10Ch. 6.3 - 27-36 Solve each equation for x e2xex6=0Ch. 6.3 - 27-36 Solve each equation for x. ln(2x+1)=2lnxCh. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - 37-38 Find the solution of the equation correct to...Ch. 6.3 - Suppose that the graph of y=log2x is drawn on a...Ch. 6.3 - The velocity of a particle that moves in a...Ch. 6.3 - The geologist C. F. Richter defined the magnitude...Ch. 6.3 - A sound so faint that it can just be heard has...Ch. 6.3 - If a bacteria population starts with 100 bacteria...Ch. 6.3 - When a camera flash goes off, the batteries...Ch. 6.3 - 47-52 Find the limit. limx3+In(x29)Ch. 6.3 - 47-52 Find the limit. limx2log5(8xx4)Ch. 6.3 - Find the limit. limx0In(cosx)Ch. 6.3 - Find the limit. limx0+In(sinx)Ch. 6.3 - 47-52 Find the limit. limx[In(1+x2)In(1+x)]Ch. 6.3 - 47-52 Find the limit. limx[In(2+x)In(1+x)]Ch. 6.3 - 53-54 Find the domain of the function....Ch. 6.3 - 53-54 Find the domain of the function....Ch. 6.3 - 55-57 Find a the domain of f and b f1 and its...Ch. 6.3 - 55-57 Find a the domain of f and b f1 and its...Ch. 6.3 - 55-57 Find a the domain of f and b f1 and its...Ch. 6.3 - a What are the values of eIn300 and In(e300)? b...Ch. 6.3 - 59-64 Find the inverse function. y=2In(x1)Ch. 6.3 - 59-64 Find the inverse function. g(x)=log4(x3+2)Ch. 6.3 - 59-64 Find the inverse function. f(x)=ex3Ch. 6.3 - 59-64 Find the inverse function. y=(Inx2),x1Ch. 6.3 - 59-64 Find the inverse function. y=32x4Ch. 6.3 - 59-64 Find the inverse function. y=1ex1+exCh. 6.3 - On what interval is the function f(x)=e3xex...Ch. 6.3 - On what interval is the curve y=2exe3x concave...Ch. 6.3 - a Show that the function f(x)=In(x+x2+1) is an odd...Ch. 6.3 - Find an equation of the tangent to the curve y=ex...Ch. 6.3 - Show that the equation x1/Inx=2 has no solution....Ch. 6.3 - Any function of the form f(x)=[g(x)]h(x), where...Ch. 6.3 - Let b1. Prove, using definitions 3.4.6 and 3.4.7,...Ch. 6.3 - a Compare the rates of growth of f(x)=x0.1 and...Ch. 6.3 - Solve the inequality In(x22x2)0.Ch. 6.3 - A prime number is a positive integer that has no...Ch. 6.4 - Explain why the natural logarithmic function y=lnx...Ch. 6.4 - 2-26 Differentiate the function. f(x)=xlnxxCh. 6.4 - 2-26 Differentiate the function. f(x)=sin(lnx)Ch. 6.4 - 2-26 Differentiate the function. f(x)=ln(sin2x)Ch. 6.4 - 2-26 Differentiate the function. f(x)=ln1xCh. 6.4 - 2-26 Differentiate the function. y=1lnxCh. 6.4 - 2-26 Differentiate the function....Ch. 6.4 - 2-26 Differentiate the function. f(x)=log10xCh. 6.4 - 2-26 Differentiate the function. g(x)=ln(xe2x)Ch. 6.4 - 2-26 Differentiate the function. g(t)=1+lntCh. 6.4 - 2-26 Differentiate the function. F(t)=(lnt2)sintCh. 6.4 - 2-26 Differentiate the function. h(x)=ln(x+x21)Ch. 6.4 - 2-26 Differentiate the function....Ch. 6.4 - 2-26 Differentiate the function. P(v)=lnv1vCh. 6.4 - 2-26 Differentiate the function. f(u)=lnu1+ln(2u)Ch. 6.4 - 2-26 Differentiate the function. y=ln|1+tt3|Ch. 6.4 - 2-26 Differentiate the function. f(x)=x5+5xCh. 6.4 - 2-26 Differentiate the function. g(x)=xsin(2x)Ch. 6.4 - 2-26 Differentiate the function. T(z)=2zlog2zCh. 6.4 - 2-26 Differentiate the function. y=ln(cscxcotx)Ch. 6.4 - 2-26 Differentiate the function. y=ln(ex+xex)Ch. 6.4 - 2-26 Differentiate the function. H(z)=lna2z2a2+z2Ch. 6.4 - 2-26 Differentiate the function. y=tan[ln(ax+b)]Ch. 6.4 - 2-26 Differentiate the function. y=log2(xlog5x)Ch. 6.4 - 2-26 Differentiate the function. G(x)=4C/xCh. 6.4 - 2-26 Differentiate the function. F(t)=3cos2tCh. 6.4 - 27-30 Find y and y. y=xlnxCh. 6.4 - 27-30 Find y and y. y=lnx1+lnxCh. 6.4 - 27-30 Find y and y. y=ln|secx|Ch. 6.4 - 27-30 Find y and y. y=ln(1+lnx)Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - 31-34 Differentiate f and find the domain of f....Ch. 6.4 - If f(x)=ln(x+lnx), find f(1)Ch. 6.4 - If f(x)=cos(lnx2), find f(1).Ch. 6.4 - 37-38 Find an equation of the tangent line to the...Ch. 6.4 - 37-38 Find an equation of the tangent line to the...Ch. 6.4 - If f(x)=sinx+lnx, find f(x). Check that your...Ch. 6.4 - Find equations of the tangent lines to the curve...Ch. 6.4 - Let f(x)=cx+ln(cosx). For what value of c is...Ch. 6.4 - Let f(x)=logb(3x2). For what value of b is f(1)=3?Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - 43-54 Use logarithmic differentiation to find the...Ch. 6.4 - Find y if y=ln(x2+y2).Ch. 6.4 - Find y if xy=yx.Ch. 6.4 - Find a formula for f(n)(x) if f(x)=ln(x1).Ch. 6.4 - Find d9dx9(x8lnx).Ch. 6.4 - 59-60 Use a graph to estimate the roots of the...Ch. 6.4 - 59-60 Use a graph to estimate the roots of the...Ch. 6.4 - Find the intervals of concavity and the inflection...Ch. 6.4 - Find the absolute minimum value of the function...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - 63-66 Discuss the curve under the guidelines of...Ch. 6.4 - If f(x)=ln(2x+xsinx), use the graphs of f,f and f...Ch. 6.4 - Investigate the family of curves f(x)=ln(x2+c)....Ch. 6.4 - The flash unit on a camera operates by storing...Ch. 6.4 - The table gives the US population from 1790 to...Ch. 6.4 - 71-82 Evaluate the integral. 243xdxCh. 6.4 - 71-82 Evaluate the integral. 03dx5x+1Ch. 6.4 - 71-82 Evaluate the integral. 12dt83tCh. 6.4 - 71-82 Evaluate the integral. 49(x+1x)2dxCh. 6.4 - 71-82 Evaluate the integral. 1ex2+x+1xdxCh. 6.4 - 71-82 Evaluate the integral. cos(lnt)tdtCh. 6.4 - 71-82 Evaluate the integral. (lnx)22dxCh. 6.4 - 71-82 Evaluate the integral. cosx2+sinxdxCh. 6.4 - 71-82 Evaluate the integral. sin2x1+cos2xdxCh. 6.4 - 71-82 Evaluate the integral. exex+1dxCh. 6.4 - 71-82 Evaluate the integral. 042sdsCh. 6.4 - 71-82 Evaluate the integral. x2x2dxCh. 6.4 - Show that cotxdx=ln|sinx|+C by a differentiating...Ch. 6.4 - Sketch the region enclosed by the curves y=lnxx...Ch. 6.4 - Find the volume of the solid obtained by rotating...Ch. 6.4 - Find the volume of the solid obtained by rotating...Ch. 6.4 - The work done by a gas when it expands from volume...Ch. 6.4 - Find f if f(x)=x2,x0,f(1)=0, and f(2)=0.Ch. 6.4 - If g is the inverse function of f(x)=2x+lnx, find...Ch. 6.4 - If f(x)=ex+lnx and h(x)=f1(x), find h(e).Ch. 6.4 - For what values of m do the line y=mx and the...Ch. 6.4 - a Find the linear approximation to f(x)=lnx near...Ch. 6.4 - Use the definition of derivative to prove that...Ch. 6.4 - Show that limn(1+xn)n=ex for any x0.Ch. 6.2Star - 1-4 Use the Laws of Logarithms to expand the...Ch. 6.2Star - 1-4 Use the Laws of Logarithms to expand the...Ch. 6.2Star - 1-4 Use the Laws of Logarithms to expand the...Ch. 6.2Star - Use the Laws of Logarithms to expand the quantity....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 5-10 Express the quantity as a single logarithm....Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 11-14 Make a rough sketch of the graph of each...Ch. 6.2Star - 15-16 Find the limit. limx3+ln(x29)Ch. 6.2Star - 15-16 Find the limit. limx[ln(2+x)ln(1+x)]Ch. 6.2Star - 17-36 Differentiate the function. f(x)=x3lnxCh. 6.2Star - 17-36 Differentiate the function. f(x)=xlnxxCh. 6.2Star - 17-36 Differentiate the function. f(x)=sin(lnx)Ch. 6.2Star - 17-36 Differentiate the function. f(x)=ln(sin2x)Ch. 6.2Star - 17-36 Differentiate the function. f(x)=ln1xCh. 6.2Star - 17-36 Differentiate the function. y=1lnxCh. 6.2Star - 17-36 Differentiate the function. f(x)=sinxln(5x)Ch. 6.2Star - Differentiate the function. h(x)=ln(x+x21)Ch. 6.2Star - 17-36 Differentiate the function. g(x)=lnaxa+xCh. 6.2Star - Differentiate the function. g(t)=1+lntCh. 6.2Star - 17-36 Differentiate the function....Ch. 6.2Star - Differentiate the function. H(z)=lna2z2a2+z2Ch. 6.2Star - 17-36 Differentiate the function. F(t)=(lnt)2sintCh. 6.2Star - 17-36 Differentiate the function. P(v)=lnv1vCh. 6.2Star - 17-36 Differentiate the function. f(u)=lnu1+ln(2u)Ch. 6.2Star - 17-36 Differentiate the function. y=(lntanx)2Ch. 6.2Star - 17-36 Differentiate the function. y=ln|2x5x2|Ch. 6.2Star - 17-36 Differentiate the function. y=lntan2xCh. 6.2Star - 17-36 Differentiate the function. y=tan[ln(ax+b)]Ch. 6.2Star - 17-36 Differentiate the function. y=ln(cscxcotx)Ch. 6.2Star - Find y and y. y=xlnxCh. 6.2Star - 37-38 Find y and y. y=ln(1+lnx)Ch. 6.2Star - 39-42 Differentiate f and find the domain of f....Ch. 6.2Star - 39-42 Differentiate f and the domain of f....Ch. 6.2Star - Differentiate f and the domain of f. f(x)=iInxCh. 6.2Star - 39-42 Differentiate f and the domain of f....Ch. 6.2Star - If f(x)=In(x+Inx), find f(1).Ch. 6.2Star - If f(x)=Inxx, find f"(e).Ch. 6.2Star - 45-46 Find f(x).Check that your answer is...Ch. 6.2Star - 45-46 Find f(x).Check that your answer is...Ch. 6.2Star - 47-48 Find an equation of tangent line to the...Ch. 6.2Star - 47-48 Find an equation of tangent line to the...Ch. 6.2Star - Find y if y=In(x2+y2)Ch. 6.2Star - Find y if Inx=ysinxCh. 6.2Star - Find a formula for f(n)(x) if f(x)=In(x1)Ch. 6.2Star - Find d9dx9(x8Inx).Ch. 6.2Star - 53-54 Use a graph to estimate the roots of the...Ch. 6.2Star - 53-54 Use a graph to estimate the roots of the...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - 55-58 Discuss the curve under the guidelines of...Ch. 6.2Star - If f(x)=In(2x+xsinx), use the graphs of f,f, and...Ch. 6.2Star - Investigate the family of curves f(x)=In(x2+c)....Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 61-64 Use logarithmic differentiation to find the...Ch. 6.2Star - 65-74 Evaluate the integral. 243xdxCh. 6.2Star - 65-74 Evaluate the integral. 03dx5x+1Ch. 6.2Star - 65-74 Evaluate the integral. 12dt83tCh. 6.2Star - Evaluate the integral. 49(x+1x)2dxCh. 6.2Star - 65-74 Evaluate the integral. 1ex2+x+1xdxCh. 6.2Star - 65-74 Evaluate the integral. e6dxxsinxCh. 6.2Star - 65-74 Evaluate the integral. (Inx)2xdxCh. 6.2Star - 65-74 Evaluate the integral. cosx2+sinxdxCh. 6.2Star - 65-74 Evaluate the integral. sin2x1+cos2xdxCh. 6.2Star - 65-74 Evaluate the integral. cos(Int)tCh. 6.2Star - Show that cotxdx=In|sinx|+C by a differentiating...Ch. 6.2Star - Sketch the region enclosed by the curves y=Inxx...Ch. 6.2Star - Find the volume of the solid obtained by rotating...Ch. 6.2Star - Find the volume of the solid obtained by rotating...Ch. 6.2Star - The work done by a gas when it expands from volume...Ch. 6.2Star - Find f if f(x)=x2, x0, f(1)=0, and f(2)=0.Ch. 6.2Star - If g is the inverse function of f(x)=2x+Inx, find...Ch. 6.2Star - a Find the linear approximation to f(x)=Inx near...Ch. 6.2Star - a By comparing areas, show that 131.5512 b Use the...Ch. 6.2Star - a Find an equation of the tangent line to the...Ch. 6.2Star - By comparing areas, show that...Ch. 6.2Star - Prove the third law of logarithms. Hint: Start by...Ch. 6.2Star - For what values of m do the line y=mx and the...Ch. 6.2Star - a Compare the rates of growth of f(x)=x0.1 and...Ch. 6.2Star - Use the definition of derivative to prove that...Ch. 6.3Star - Sketch, by hand, the graph of the function f(x)=ex...Ch. 6.3Star - 2-4 Simplify each expression. a eIn15b In(1/e2)Ch. 6.3Star - Simplify each expression. a eIn2b eIn(Ine3)Ch. 6.3Star - 2-4 Simplify each expression. a Inesinxb ex+InxCh. 6.3Star - Solve each equation for x. a e74x=6b In(3x10)=2Ch. 6.3Star - 5-12 Solve each equation for x. ln(x21)=3Ch. 6.3Star - Solve each equation for x. a e3x+1=kb...Ch. 6.3Star - Solve each equation for x. a ln(lnx)=1b eex=10Ch. 6.3Star - 5-12 Solve each equation for x. ee2x=1Ch. 6.3Star - 5-12 Solve each equation for x. 10(1+ex)1=3Ch. 6.3Star - 5-12 Solve each equation for x. e2xex6=0Ch. 6.3Star - 5-12 Solve each equation for x. ln(2x+1)=2lnxCh. 6.3Star - Find the solution of the equation correct to four...Ch. 6.3Star - Find the solution of the equation correct to four...Ch. 6.3Star - Solve each inequality for x. a lnx0b ex5Ch. 6.3Star - Solve each inequality for x. a 1e3x12b 12lnx3Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 17-20 Make a rough sketch of the graph of the...Ch. 6.3Star - 21-22 Find a the domain of f and b f1 and its...Ch. 6.3Star - 21-22 Find a the domain of f and b f1 and its...Ch. 6.3Star - 23-26: Find the inverse function y=2ln(x1)Ch. 6.3Star - 23-26: Find the inverse function y=(lnx)2,x1Ch. 6.3Star - 23-26: Find the inverse function f(x)=ex3Ch. 6.3Star - 23-26: Find the inverse function y=1ex1+exCh. 6.3Star - 27-32 Find the limit. limxe3xe3xe3x+e3xCh. 6.3Star - 27-32 Find the limit. limxex2Ch. 6.3Star - 27-32 Find the limit. limx2+e3/(2x)Ch. 6.3Star - 27-32 Find the limit. limx2e3/(2x)Ch. 6.3Star - 27-32 Find the limit. limx(e2xcosx)Ch. 6.3Star - 27-32 Find the limit. limx(/2)+etanxCh. 6.3Star - 33-52 Differentiate the function. f(x)=e5Ch. 6.3Star - 33-52 Differentiate the function. k(r)=er+reCh. 6.3Star - 33-52 Differentiate the function. f(x)=(3x25x)exCh. 6.3Star - 33-52 Differentiate the function. y=ex1exCh. 6.3Star - 33-52 Differentiate the function. y=eax3Ch. 6.3Star - 33-52 Differentiate the function. g(x)=ex2xCh. 6.3Star - 33-52 Differentiate the function. y=etanCh. 6.3Star - 33-52 Differentiate the function. V(t)=4+ttetCh. 6.3Star - 33-52 Differentiate the function. f(x)=x2exx2+exCh. 6.3Star - 33-52 Differentiate the function. y=x2e1/xCh. 6.3Star - 33-52 Differentiate the function. y=x2e3xCh. 6.3Star - 33-52 Differentiate the function. f(t)=tan(1+e2t)Ch. 6.3Star - 33-52 Differentiate the function. f(t)=eatsinbtCh. 6.3Star - 33-52 Differentiate the function. f(z)=ez/(z1)Ch. 6.3Star - 33-52 Differentiate the function. F(t)=etsin2tCh. 6.3Star - 33-52 Differentiate the function....Ch. 6.3Star - 33-52 Differentiate the function. g(u)=esecu2Ch. 6.3Star - 33-52 Differentiate the function. y=1+xe2xCh. 6.3Star - 33-52 Differentiate the function. y=cos(1e2x1+e2x)Ch. 6.3Star - 33-52 Differentiate the function....Ch. 6.3Star - 53-54 Find an equation of the tangent line to the...Ch. 6.3Star - 53-54 Find an equation of the tangent line to the...Ch. 6.3Star - Find y if ex/y=xyCh. 6.3Star - Find an equation of the tangent line to the curve...Ch. 6.3Star - Show that the function y=ex+ex/2 satisfies the...Ch. 6.3Star - Show that the function y=Aex+Bxex satisfies the...Ch. 6.3Star - For what values of r does the function y=erx...Ch. 6.3Star - Find the values of for which y=ex satisfies the...Ch. 6.3Star - If f(x)=e2x, find a formula for f(n)(x).Ch. 6.3Star - Find the thousandth derivative of f(x)=xex.Ch. 6.3Star - a Use the Intermediate Value theorem to show that...Ch. 6.3Star - Use a graph to find an initial approximation to...Ch. 6.3Star - Under certain circumstances a rumor spreads...Ch. 6.3Star - An object is attached to the end of a vibrating...Ch. 6.3Star - Find the absolute maximum value of the function...Ch. 6.3Star - Find the absolute minimum value of the function...Ch. 6.3Star - 69-70 Find the absolute maximum and absolute...Ch. 6.3Star - 69-70 Find the absolute maximum and absolute...Ch. 6.3Star - 71-72 Find a the intervals of increase or...Ch. 6.3Star - 71-72 Find a the intervals of increase or...Ch. 6.3Star - 73-75 Discuss the curve using the guidelines of...Ch. 6.3Star - 73-75 Discuss the curve using the guidelines of...Ch. 6.3Star - 73-75 Discuss the curve using the guidelines of...Ch. 6.3Star - Let g(x)=ecx+f(x) and h(x)=ekxf(x), where f(0)=3,...Ch. 6.3Star - A drug response curve describes the level of...Ch. 6.3Star - After an antibiotic tablet is taken, the...Ch. 6.3Star - After the consumption of an alcoholic beverage,...Ch. 6.3Star - 80-81. Draw a graph of f that shows all the...Ch. 6.3Star - 80-81. Draw a graph of f that shows all the...Ch. 6.3Star - The family of bell-shaped curves y=12e(x)2/(22)...Ch. 6.3Star - 83-94 Evaluate the integral. 01(xe+ex)dxCh. 6.3Star - 83-94 Evaluate the integral. 55edxCh. 6.3Star - 83-94 Evaluate the integral. 02dxexCh. 6.3Star - 83-94 Evaluate the integral. x2ex3dxCh. 6.3Star - 83-94 Evaluate the integral. ex1+exdxCh. 6.3Star - 83-94 Evaluate the integral. (1+ex)2exdxCh. 6.3Star - 83-94 Evaluate the integral. (ex+ex)2dxCh. 6.3Star - 83-94 Evaluate the integral. ex(4+ex)5dxCh. 6.3Star - 83-94 Evaluate the integral. eu(1eu)2duCh. 6.3Star - 83-94 Evaluate the integral. esincosdCh. 6.3Star - 83-94 Evaluate the integral. 12e1/xx2dxCh. 6.3Star - 83-94 Evaluate the integral. 011+exexdxCh. 6.3Star - Find, correct to three decimal places, the area of...Ch. 6.3Star - Find f(x) if f(x)=3ex+5sinx,f(0)=1, and f(0)=2.Ch. 6.3Star - Find the volume of the solid obtained by rotating...Ch. 6.3Star - Find the volume of the solid obtained by rotating...Ch. 6.3Star - The error function erf(x)=20xet2dt is used in...Ch. 6.3Star - Show that the function y=ex2erf(x) satisfies the...Ch. 6.3Star - An oil storage tank ruptures at time t = 0 and oil...Ch. 6.3Star - A bacteria population starts with 400 bacteria and...Ch. 6.3Star - Dialysis treatment removes urea and other waste...Ch. 6.3Star - The rate of growth of a fish population was...Ch. 6.3Star - If you graph the function f(x)=1e1/x1+e1/x youll...Ch. 6.3Star - Graph several members of the family of functions...Ch. 6.3Star - Prove the second law of exponents see 7.Ch. 6.3Star - Prove the third law of exponents see 7.Ch. 6.3Star - a Show that ex1+xifx0. Hint: Show that...Ch. 6.3Star - a Use the inequality of Exercise 109a to show...Ch. 6.3Star - a Use mathematical induction to prove that for x0...Ch. 6.3Star - This exercise illustrates Exercise 111c for the...Ch. 6.4Star - a Write an equation that defines bx when b is a...Ch. 6.4Star - a If b is a positive number and b1, how is logbx...Ch. 6.4Star - 3-6 Write the expression as a power of e. 4Ch. 6.4Star - 3-6 Write the expression as a power of e. x5Ch. 6.4Star - 3-6 Write the expression as a power of e. 10x2Ch. 6.4Star - 3-6 Write the expression as a power of e....Ch. 6.4Star - 7-10 Evaluate the expression. a log232 b log82Ch. 6.4Star - 7-10 Evaluate the expression. a log1010 b...Ch. 6.4Star - 7-10 Evaluate the expression. a log1040+log102.5 b...Ch. 6.4Star - 7-10 Evaluate the expression. a loga1a b...Ch. 6.4Star - 11-12 Graph the given functions on a common...Ch. 6.4Star - 11-12 Graph the given functions on a common...Ch. 6.4Star - Use Formula 6 to evaluate each logarithm correct...Ch. 6.4Star - 14-16 Use Formula 6 to graph the given functions...Ch. 6.4Star - 14-16 Use Formula 6 to graph the given functions...Ch. 6.4Star - 14-16 Use Formula 6 to graph the given functions...Ch. 6.4Star - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.4Star - 17-18 Find the exponential function f(x)=Cbx whose...Ch. 6.4Star - a Suppose the graphs of f(x)=x2 and g(x)=2xare...Ch. 6.4Star - Compare the rates of growth of the functions...Ch. 6.4Star - 21-24 Find the limit. limx(1.001)xCh. 6.4Star - 21-24 Find the limit. limx(1.001)xCh. 6.4Star - 21-24 Find the limit. limt2t2Ch. 6.4Star - 21-24 Find the limit. limx3+log10(x25x+6)Ch. 6.4Star - 25-42 Differentiate the function. f(x)=x5+5xCh. 6.4Star - 25-42 Differentiate the function. g(x)=xsin(2x)Ch. 6.4Star - 25-42 Differentiate the function. G(x)=4c/xCh. 6.4Star - 25-42 Differentiate the function. F(t)=3cos2tCh. 6.4Star - 25-42 Differentiate the function. L(v)=tan(4v2)Ch. 6.4Star - 25-42 Differentiate the function. G(u)=(1+10lnu)6Ch. 6.4Star - 25-42 Differentiate the function. f(x)=log2(13x)Ch. 6.4Star - 25-42 Differentiate the function. f(x)=log10xCh. 6.4Star - 25-42 Differentiate the function. y=xlog4sinxCh. 6.4Star - 25-42 Differentiate the function. y=log2(xlog5x)Ch. 6.4Star - 25-42 Differentiate the function. y=xxCh. 6.4Star - 25-42 Differentiate the function. y=xcosxCh. 6.4Star - 25-42 Differentiate the function. y=xsinxCh. 6.4Star - 25-42 Differentiate the function. y=(x)xCh. 6.4Star - 25-42 Differentiate the function. y=(cosx)xCh. 6.4Star - 25-42 Differentiate the function. y=(sinx)lnxCh. 6.4Star - 25-42 Differentiate the function. y=(tanx)1/xCh. 6.4Star - 25-42 Differentiate the function. y=(lnx)cosxCh. 6.4Star - Find an equation of the tangent line to the curve...Ch. 6.4Star - If f(x)=xcosx, find f(x). Check that your answer...Ch. 6.4Star - 45-50 Evaluate the integral. 042sdsCh. 6.4Star - 45-50 Evaluate the integral. (x5+5x)dxCh. 6.4Star - 45-50 Evaluate the integral. log10xxdxCh. 6.4Star - 45-50 Evaluate the integral. x2x2dxCh. 6.4Star - 45-50 Evaluate the integral. 3sincosdCh. 6.4Star - 45-50 Evaluate the integral. 2x2x+1dxCh. 6.4Star - Find the area of the region bounded by the curves...Ch. 6.4Star - The region under the curve y=10x from x=0 to x=1...Ch. 6.4Star - Use a graph to find the root of the equation...Ch. 6.4Star - Find y if xy=yx.Ch. 6.4Star - Find the inverse function of g(x)=log4(x3+2).Ch. 6.4Star - Calculate limx0+xlnxCh. 6.4Star - The geologist C. F. Richter defined the magnitude...Ch. 6.4Star - A sound so faint that it can just be heard has...Ch. 6.4Star - Referring to Exercise 58, find the rate of change...Ch. 6.4Star - According to the Beer-Lambert Law, the light...Ch. 6.4Star - After the consumption of an alcoholic beverage,...Ch. 6.4Star - In this section we modeled the world population...Ch. 6.4Star - Use the graph of V in Figure 9 to estimate the...Ch. 6.4Star - A researcher is trying to determine the doubling...Ch. 6.4Star - The flash unit on a camera operates by storing...Ch. 6.4Star - The table gives the US population from 1790 to...Ch. 6.4Star - Prove the second law of exponents see 3.Ch. 6.4Star - Prove the fourth law of exponents see 3.Ch. 6.4Star - Deduce the following laws of logarithms from 3: a...Ch. 6.4Star - Show that limn(1+xn)n=ex for any x0.Ch. 6.5 - A population of protozoa develops with a constant...Ch. 6.5 - A common inhabitant of human intestines is the...Ch. 6.5 - A bacteria culture initially contains 100 cells...Ch. 6.5 - A bacteria culture grows with constant relative...Ch. 6.5 - The table gives estimates of the world population,...Ch. 6.5 - The table gives the population of Indonesia, in...Ch. 6.5 - Experiments show that if the chemical reaction...Ch. 6.5 - Strontium-90 has a half-life of 28 days. a A...Ch. 6.5 - The half-life of cesium-137 is 30 years. Suppose...Ch. 6.5 - A sample of tritium-3 decayed to 94.5 of its...Ch. 6.5 - Scientists can determine the age of ancient...Ch. 6.5 - Dinosaur fossils are too old to be reliably dated...Ch. 6.5 - Dinosaur fossils are often dated by using an...Ch. 6.5 - A curve passes through the point (0,5) and has the...Ch. 6.5 - A roast turkey is taken from an oven when its...Ch. 6.5 - In a murder investigation, the temperature of the...Ch. 6.5 - When a cold drink is taken from a refrigerator,...Ch. 6.5 - A freshly brewed cup of coffee has temperature 95C...Ch. 6.5 - The rate of change of atmospheric pressure P with...Ch. 6.5 - a If 1000 is borrowed at 8 interest, find the...Ch. 6.5 - a If 3000 is invested at 5 interest, find the...Ch. 6.5 - a How long will it take an investment to double in...Ch. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Find the exact value of each expression. a tan13 b...Ch. 6.6 - Find the exact value of each expression. a csc12 b...Ch. 6.6 - Find the exact value of each expression. a cot1(3)...Ch. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Find the exact value of each expression. a...Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Find the exact value of each expression....Ch. 6.6 - Prove that cos(sin1x)=1x2Ch. 6.6 - 12-14 Simplify the each expression. tan(sin1(x))Ch. 6.6 - 12-14 Simplify the each expression. sin(tan1(x))Ch. 6.6 - 12-14 Simplify the each expression. sin(2arccosx)Ch. 6.6 - 15-16 Graph the given functions on the same...Ch. 6.6 - 15-16 Graph the given functions on the same...Ch. 6.6 - Prove Formula 6 for the derivatives of cos1 by the...Ch. 6.6 - a Prove that sin1x+cos1x=/2 b Use part a to prove...Ch. 6.6 - Prove that ddt(cot1x)=11+x2.Ch. 6.6 - Prove that ddt(sec1x)=1xx21Ch. 6.6 - Prove that ddt(csc1x)=1xx21Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - Find the derivative of the function. Simplify...Ch. 6.6 - 36-37 Find the derivative of the function. Find...Ch. 6.6 - 36-37 Find the derivative of the function. Find...Ch. 6.6 - Find y if tan1(x2y)=x+xy2.Ch. 6.6 - If g(x)=xsin1(x/4)+16x2, find g(2).Ch. 6.6 - Find an equation of the tangent line to the curve...Ch. 6.6 - Find f(x). Check that your answer is reasonable by...Ch. 6.6 - 41-42 Find f(x). Check that your answer is...Ch. 6.6 - 43-46 Find the limit. limx1+sin1xCh. 6.6 - 43-46 Find the limit. limx(1+x21+2x2)Ch. 6.6 - 43-46 Find the limit. limxarctan(ex)Ch. 6.6 - 43-46 Find the limit. limx0+tan1(Inx)Ch. 6.6 - Where should the point P be chosen on the line...Ch. 6.6 - A painting in an art gallery has height h and is...Ch. 6.6 - A ladder 10 ft long leans against a vertical wall....Ch. 6.6 - A lighthouse is located on a small island, 3 km...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - 51-54 Sketch the curve using the guidelines of...Ch. 6.6 - If f(x)=arctan(cos(3arcsinx)), use the graphs of...Ch. 6.6 - Investigate the family of curves given by...Ch. 6.6 - Find the most general antiderivative of the...Ch. 6.6 - Find g(t) if g(t)=2/1t2 and g(1)=5.Ch. 6.6 - Evaluate the integral. 1/3381+x2dxCh. 6.6 - Evaluate the integral. 1/21/261p2dpCh. 6.6 - Evaluate the integral. 01/2sin1x1x2dxCh. 6.6 - Evaluate the integral. 03/4dx1+16x2Ch. 6.6 - Evaluate the integral. 1+x1+x2dxCh. 6.6 - Evaluate the integral. 0/2sinx1+cos2xdxCh. 6.6 - Evaluate the integral. dx1x2sin1xCh. 6.6 - Evaluate the integral. 1xx24dxCh. 6.6 - Evaluate the integral. t21t6dtCh. 6.6 - Evaluate the integral. e2x1e4xdxCh. 6.6 - Evaluate the integral. dxx(1+x)Ch. 6.6 - Evaluate the integral. x1+x4dxCh. 6.6 - Use the method of Example 8 to show that, if a0,...Ch. 6.6 - The region under the curve y=1/x2+4 from x=0 to...Ch. 6.6 - Evaluate 01sin1xdx interpreting it as an area and...Ch. 6.6 - Prove that, for xy1,arctanx+arctany=arctanx+y1xy...Ch. 6.6 - Use the result of Exercise 74 to prove the...Ch. 6.6 - a Sketch the graph of the function...Ch. 6.6 - Use the method of Example 6 to prove the identity...Ch. 6.6 - Prove the identity arcsinx1x+1=2arctanx2Ch. 6.6 - Some authors define y=sec1xsecy=x and...Ch. 6.6 - Let f(x)=x arctan (1/x) if x0 and f(0)=0. a Is f...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 1-6 Find the numerical value of each expression. a...Ch. 6.7 - 7-19 Prove the following identity sinh(x)=sinhx...Ch. 6.7 - 7-19 Prove the following identity cosh(x)=coshx...Ch. 6.7 - 7-19 Prove the following identity coshx+sinhx=exCh. 6.7 - 7-19 Prove the following identity coshxsinhx=exCh. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity coth2x1=csch2xCh. 6.7 - 7-19 Prove the identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - Prove the following identity cosh2x=coh2x+sinh2xCh. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - 7-19 Prove the following identity...Ch. 6.7 - If tanhx=1213, find the values of the other...Ch. 6.7 - If coshx=53 and x0, find the values of the other...Ch. 6.7 - a Use the graphs of sinh, cosh, and tanh in...Ch. 6.7 - Use the definitions of the hyperbolic functions to...Ch. 6.7 - Prove the formulas given in Table 1 for the...Ch. 6.7 - Give an alternative solution to Example 3 by...Ch. 6.7 - Prove Equation 4.Ch. 6.7 - Prove Equation 5 using a the method of Example 3...Ch. 6.7 - For each of the following functions i give a...Ch. 6.7 - Prove the formulas given in Table 6 for the...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - 30-45 Find the derivative. Simplify where...Ch. 6.7 - Show that ddx1+tanhx1tanhx4=12ex/2Ch. 6.7 - Show that ddxarctan(tanhx)=sech2xCh. 6.7 - The Gateway Arch in St. Louis was designed by Eero...Ch. 6.7 - If a water wave with length L moves with velocity...Ch. 6.7 - A flexible cable always hangs in the shape of a...Ch. 6.7 - A telephone line hangs between two poles 14 m...Ch. 6.7 - Using principles from physics it can be shown that...Ch. 6.7 - A cable with linear density =2kg/m is strung from...Ch. 6.7 - A model for the velocity of a falling object after...Ch. 6.7 - a Show that any function of the form...Ch. 6.7 - If x=ln(sec+tan), show that sec=coshx.Ch. 6.7 - At what point of the curve y=coshx does the...Ch. 6.7 - Investigate the family of functions...Ch. 6.7 - 59-67 Evaluate the integral. sinhxcosh2xdxCh. 6.7 - 59-67 Evaluate the integral. sinh(1+4x)dxCh. 6.7 - 59-67 Evaluate the integral. sinhxxdxCh. 6.7 - 59-67 Evaluate the integral. tanhxdxCh. 6.7 - 59-67 Evaluate the integral. coshxcosh2x1dxCh. 6.7 - 59-67 Evaluate the integral. sech2x2+tanhxdxCh. 6.7 - 59-67 Evaluate the integral. 461t29dtCh. 6.7 - 59-67 Evaluate the integral. 01116t2+1dtCh. 6.7 - 59-67 Evaluate the integral. ex1e2xdxCh. 6.7 - Estimate the value of the number c such that the...Ch. 6.7 - a Use Newtons method or a graphing device to find...Ch. 6.7 - Show that the area of the shaded hyperbolic sector...Ch. 6.7 - Show that if a0 and b0, then there exist numbers ...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 1-4 Given that...Ch. 6.8 - 5-6 Use the graphs of f and g and their tangent...Ch. 6.8 - 5-6 Use the graphs of f and g and their tangent...Ch. 6.8 - The graph of a function f and its tangent line at...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. Use IHospitals Rule where...Ch. 6.8 - 8-68 Find the limit. 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Use IHospitals Rule where...Ch. 6.8 - 69-70 Use a graph to estimate the value of the...Ch. 6.8 - 69-70 Use a graph to estimate the value of the...Ch. 6.8 - 71-72 Illustrate IHospitals Rule by graphing both...Ch. 6.8 - 71-72 Illustrate IHospitals Rule by graphing both...Ch. 6.8 - Prove that limxexxn= for any positive integer n....Ch. 6.8 - Prove that limxlnxxp=0 for any number p0. This...Ch. 6.8 - 75-76 What happens if you try to use IHospitals...Ch. 6.8 - 75-76 What happens if you try to use IHospitals...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 77-82 Use lHospitals Rule to help sketch the...Ch. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - 83-85 a Graph the function. b Use lHospitals Rule...Ch. 6.8 - Investigate the family of curves given by...Ch. 6.8 - Investigate the family of curves f(x)=excx. In...Ch. 6.8 - If an object with mass m is dropped from rest, one...Ch. 6.8 - If an initial amount A0 of money is invested at an...Ch. 6.8 - Light enters the eye through the pupil and strikes...Ch. 6.8 - Some populations initially grow exponentially but...Ch. 6.8 - A metal cable has radius r and is covered by...Ch. 6.8 - In Section 4.3 we investigated the Fresnel...Ch. 6.8 - Suppose that the temperature in a long thin rod...Ch. 6.8 - The first appearance in print of 1Hospitals Rule...Ch. 6.8 - The figure shows a sector of a circle with central...Ch. 6.8 - Evaluate limx[xx2ln(1+xx)]Ch. 6.8 - Suppose f is a positive function. If limxaf(x) and...Ch. 6.8 - If f is continuous, f(2)=0, and f(2)=7, evaluate...Ch. 6.8 - For what values of a and b is the following...Ch. 6.8 - If f is continuous, use lHospitals Rule to show...Ch. 6.8 - If f is continuous, show that...Ch. 6.8 - Let f(x)={e1/x2ifx00ifx0 a Use the definition of...Ch. 6.8 - Let f(x)={|x|xifx01ifx=0 a Show that f is...Ch. 6.R - a What is a one-to-one function? How can you tell...Ch. 6.R - a What are the domain and range of the natural...Ch. 6.R - a How is the inverse sine function f(x)=sin1x...Ch. 6.R - Write the definitions of the hyperbolic functions...Ch. 6.R - State the derivative of each function. a y=ex b...Ch. 6.R - a How is the number e defined? b Express e as a...Ch. 6.R - a Write a differential equation that expresses the...Ch. 6.R - a What does lHospitals rule say? b How can you use...Ch. 6.R - State whether each of the following limit forms is...Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - Determine whether the statement is true or false....Ch. 6.R - The graph of f is shown. Is f one-to-one? Explain.Ch. 6.R - The graph of g is given. a Why is g one-to-one? b...Ch. 6.R - Suppose f is one-to-one, f(7)=(3), and f(7)=8....Ch. 6.R - Find the inverse function of f(x)=x+12x+1.Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - 5-9 Sketch a rough graph of the function without...Ch. 6.R - Let b1. For large values of x, which of the...Ch. 6.R - 11-12 Find the exact value of each expression. a...Ch. 6.R - 11-12 Find the exact value of each expression. a...Ch. 6.R - 13-20 Solve the equation for x. lnx=13Ch. 6.R - 13-20 Solve the equation for x. ex=13Ch. 6.R - 13-20 Solve the equation for x. eex=17Ch. 6.R - 13-20 Solve the equation for x. ln(1+ex)=3Ch. 6.R - 13-20 Solve the equation for x. ln(x+1)+ln(x1)=1Ch. 6.R - 13-20 Solve the equation for x. log5(cx)=dCh. 6.R - 13-20 Solve the equation for x. tan1x=1Ch. 6.R - 13-20 Solve the equation for x. sinx=0.3Ch. 6.R - 21-47 Differentiate. f(t)=t2lntCh. 6.R - 21-47 Differentiate. g(t)=et1+etCh. 6.R - 21-47 Differentiate. h()=etan2Ch. 6.R - 21-47 Differentiate. h(u)=10uCh. 6.R - 21-47 Differentiate. y=ln|sec5x+tan5x|Ch. 6.R - 21-47 Differentiate. y=xcos1xCh. 6.R - 21-47 Differentiate. y=xtan1(4x)Ch. 6.R - 21-47 Differentiate. y=emxcosnxCh. 6.R - 21-47 Differentiate. y=ln(sec2x)Ch. 6.R - 21-47 Differentiate. y=tln(t4)Ch. 6.R - 21-47 Differentiate. y=e1/xx2Ch. 6.R - 21-47 Differentiate. y=(arcsin2x)2Ch. 6.R - 21-47 Differentiate. y=3xlnxCh. 6.R - 21-47 Differentiate. y=ecosx+cos(ex)Ch. 6.R - 21-47 Differentiate. H(v)=vtanv1Ch. 6.R - 21-47 Differentiate. F(z)=log10(1+z2)Ch. 6.R - 21-47 Differentiate. y=xsinh(x2)Ch. 6.R - 21-47 Differentiate. y=(cosx)xCh. 6.R - 21-47 Differentiate. y=lnsinx12sin2xCh. 6.R - 21-47 Differentiate. y=arctan(arcsinx)Ch. 6.R - 21-47 Differentiate. y=ln(1x)+1lnxCh. 6.R - 21-47 Differentiate. xey=y1Ch. 6.R - 21-47 Differentiate. y=ln(cosh3x)Ch. 6.R - 21-47 Differentiate. y=(x2+1)4(2x+1)3(3x1)5Ch. 6.R - 21-47 Differentiate. y=cosh1(sinhx)Ch. 6.R - 21-47 Differentiate. y=xtanh1xCh. 6.R - 21-47 Differentiate. y=cos(etan3x)Ch. 6.R - Show that ddx(12tan1x+14ln(x+1)2x2+1)=1(1+x)(1+x2)Ch. 6.R - 49-52 Find f in terms of g f(x)=eg(x)Ch. 6.R - 49-52 Find f in terms of g f(x)=g(ex)Ch. 6.R - 49-52 Find f in terms of g f(x)=ln|g(x)|Ch. 6.R - 49-52 Find f in terms of g f(x)=g(lnx)Ch. 6.R - 53-54 Find f(n)(x). f(x)=2xCh. 6.R - 53-54 Find f(n)(x). f(x)=ln(2x)Ch. 6.R - Use mathematical induction to show that if...Ch. 6.R - Find y if y=x+arctanyCh. 6.R - 57-58 Find an equation of the tangent to the curve...Ch. 6.R - 57-58 Find an equation of the tangent to the curve...Ch. 6.R - At what point on the curve y=[ln(x+4)]2 is the...Ch. 6.R - If f(x)=xesinx, find f(x). Graph f and f on the...Ch. 6.R - a Find an equation of the tangent to the curve...Ch. 6.R - The function C(t)=K(eatebt),a, b, and K are...Ch. 6.R - 63-78 Evaluate the limit. limxe3xCh. 6.R - 63-78 Evaluate the limit. limxln(100x2)Ch. 6.R - 63-78 Evaluate the limit. limx3e2/(x3)Ch. 6.R - 63-78 Evaluate the limit. limxarctan(x3x)Ch. 6.R - 63-78 Evaluate the limit. limx0+ln(sinhx)Ch. 6.R - 63-78 Evaluate the limit. limxexsinxCh. 6.R - 63-78 Evaluate the limit. limx1+2x12xCh. 6.R - 63-78 Evaluate the limit. limx(1+4x)xCh. 6.R - 63-78 Evaluate the limit. limx0ex1tanxCh. 6.R - 63-78 Evaluate the limit. limx01cosxx2+xCh. 6.R - 63-78 Evaluate the limit. limx0e2xe2xln(x+1)Ch. 6.R - 63-78 Evaluate the limit. limxe2xe2xln(x+1)Ch. 6.R - 63-78 Evaluate the limit. limx(x2x3)e2xCh. 6.R - 63-78 Evaluate the limit. limx0+x2lnxCh. 6.R - 63-78 Evaluate the limit. limx1+(xx11lnx)Ch. 6.R - 63-78 Evaluate the limit. limx(/2)(tanx)cosxCh. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - 79-84 Sketch the curve using the guidelines of...Ch. 6.R - Investigate the family of curves given by...Ch. 6.R - Investigate the family of functions...Ch. 6.R - An equation of motion of the form s=Aectcos(t+)...Ch. 6.R - a Show that there is exactly one root of the...Ch. 6.R - A bacteria culture contains 200 cells initially...Ch. 6.R - Cobalt-60 has a half-life of 5.24 years. a Find...Ch. 6.R - The biologist G. F. Gause conducted an experiment...Ch. 6.R - 92-105 Evaluate the integral. 04116+t2dtCh. 6.R - 92-105 Evaluate the integral. 01ye2y2dyCh. 6.R - 92-105 Evaluate the integral. 25dr1+2rCh. 6.R - 92-105 Evaluate the integral. 01ex1+e2xdxCh. 6.R - 92-105 Evaluate the integral. 0/2cosx1+sin2xdxCh. 6.R - 92-105 Evaluate the integral. exxdxCh. 6.R - 92-105 Evaluate the integral. sin(lnx)xdxCh. 6.R - 92-105 Evaluate the integral. x+1x2+2xdxCh. 6.R - 92-105 Evaluate the integral. csc2x1+cotxdxCh. 6.R - 92-105 Evaluate the integral. tanxln(cosx)dxCh. 6.R - 92-105 Evaluate the integral x1x4dxCh. 6.R - 92-105 Evaluate the integral 2tansec2dCh. 6.R - 92-105 Evaluate the integral sinhauduCh. 6.R - 92-105 Evaluate the integral (1xx)2dxCh. 6.R - 106-108 Use properties of integrals to prove the...Ch. 6.R - 106-108 Use properties of integrals to prove the...Ch. 6.R - 106-108 Use properties of integrals to prove the...Ch. 6.R - 109-110 Find f(x). f(x)=1xessdsCh. 6.R - 109-110 Find f(x). f(x)=lnx2xet2dtCh. 6.R - Find the average value of the function f(x)=1/x on...Ch. 6.R - Find the area of the region bounded by the curves...Ch. 6.R - Find the volume of the solid obtained by rotating...Ch. 6.R - If f(x)=x+x2+ex, find (f1)(1).Ch. 6.R - If f(x)=lnx+tan1x, find (f1)(/4).Ch. 6.R - What is the area of the largest rectangle in the...Ch. 6.R - What is the area of the largest triangle in the...Ch. 6.R - Evaluate 01exdxwithout using the Fundamental...Ch. 6.R - If, F(x)=abtxdt, where a, b0, then, by the...Ch. 6.R - Show that cos{arctan[sin(arccotx)]}=x2+1x2+2Ch. 6.R - If f is a continuous function such that...Ch. 6.R - The figure shows two regions in the first...Ch. 6.P - If a rectangle has its base on the x-axis and two...Ch. 6.P - Prove that log25 is an irrational number.Ch. 6.P - Does the function f(x)=e10|x2|x2 have an absolute...Ch. 6.P - If 04e(x2)4dx=k, find the value of 04xe(x2)4dx.Ch. 6.P - Show that dndxn(eaxsinbx)=rneaxsin(bx+n) where a...Ch. 6.P - Show that sin1(tanhx)=tan1(sinhx).Ch. 6.P - Show that, for x0, x1+x2tan1xxCh. 6.P - Suppose f is continuous, f(0)=0,f(1)=1,f(x)0, and...Ch. 6.P - Show that f(x)=1x1+t3dt is one-one and find...Ch. 6.P - If y=xa212a21arctansinxa+a21+cosx Show that...Ch. 6.P - For what value of a is the following equation...Ch. 6.P - Evaluate limx(x+2)1/xx1/x(x+3)1/xx1/xCh. 6.P - Evaluate. Assume that the integrand is defined and...Ch. 6.P - Sketch the set of all points (x,y) such that...Ch. 6.P - Prove that cosh(sinhx)sinh(coshx) for all xCh. 6.P - Show that, for all positive value of x and y,...Ch. 6.P - For what value of k does the equation e2x=kx have...Ch. 6.P - For which positive numbers a is it true that ax1+x...Ch. 6.P - For which positive numbers a does the curve y=ax...Ch. 6.P - For what values of c does the curve y=cx3+ex have...
Finding the Domain In Exercises 41-46, find the domain of the function. f(x)=13+ex
Discriminant Use the discriminant to determine the number of real solutions of the equation. Do not solve the e...
Graph the functions f(x,y)=x2+y2 f(x,y)=ex2+y2 f(x,y)=lnx2+y2 f(x,y)=sin(x2+y2) and f(x,y)=1x2+y2 In general, i...
In Exercises 516, evaluate the given quantity. log1/212
Express the given quantity as a single logarithm. 39. ln 10 + 2 ln 5
Find the slope of the tangent line to the given curve at the point corresponding to the specified value of the ...
Finding Limits In Exercises 93-110, find the limit (if it exists). limx0(x+x)3(xx)(x3x)x
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Evaluate the limit, if it exists. 19. limx2x+2x3+8
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For Problems 1-10, answer true or false. The absolute value of zero does not exist.
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Phone42.com / Smartphones / Huawei / Huawei G7 Plus
Huawei G7 Plus (2015) review
Android OS v5.1.1 (Lollipop)
Qualcomm Snapdragon 616 MSM8939v2
Huawei announced the launch of the G7 Plus smartphone in 2015. The manufacturer is offering the Huawei G7 Plus phone with 5.5 inches display, Qualcomm Snapdragon 616 MSM8939v2 chipset, 3 GB of RAM and 32 GB of internal storage.
The Huawei G7 Plus comes with Android OS v5.1.1 (Lollipop) out of the box, and a Li-Po 3000 mAh, non-removable battery. The 5.5 inches phone comes with IPS display (1080 x 1920 px). The IPS display provides enhanced features, such as optimal viewing angles, color accuracy, invariable color reproduction and better power consumption.
Add Huawei G7 Plus to your comparison
Huawei G7 Plus specifications
The weight of Huawei G7 Plus is about 5.89 oz with battery, which is average compared to most of the smartphones with same size. The dimensions of this Huawei phone are average (6 x 3.01 x 0.3 inches).
6 x 3.01 x 0.3 inches
The Huawei G7 Plus comes with Android OS v5.1.1 (Lollipop) out of the box, but it is upgradable to the next OS.
The size of G7 Plus screen is measured diagonally, from corner to corner. The 5.5 inches IPS display of Huawei G7 Plus with 1080 x 1920 px resolution is multitouch capable.
The internal memory of Huawei G7 Plus (3 GB) cannot be expanded, but the internal storage (32 GB) can be expanded with a compatible microSD card.
The camera of the G7 Plus is equipped with autofocus. An autofocus (or AF) optical system uses a sensor, a control system and a motor to focus on an automatically or manually selected point or area. Very few Android cameras come without autofocus.
The Huawei G7 Plus supports 2G, 3G and 4G/LTE networks. This phone has a built-in GPS. GPS is a highly accurate navigation system using signals from satellites to determine a location on the Earth's surface, irrespective of weather conditions. Most phones have a GPS unit on board. The G7 Plus comes with NFC (Near Field Communication) functionality. Near Field Communication (NFC) is a short-range wireless connectivity technology that makes life easier and more convenient for consumers around the world by making it simpler to make transactions, exchange digital content, and connect electronic devices with a touch. The G7 Plus phone has built-in FM radio. The built-in FM Radio is great for listening to your favorite radio station.
The Li-Po 3000 mAh, non-removable battery gives the smartphone a good battery backup. The lithium polymer (Li-Po) battery is a thin, light-weight, rechargeable battery. No periodic discharge is needed and charging can be done at random. The battery of G7 Plus isn't removable without voiding the warranty.
Smartphones today come with a wealth of sensors to facilitate a better user experience. The accelerometer is a sensor that measures the tilting motion and orientation of the phone. This Huawei phones comes with proximity sensor. This proximity sensor detects how close the phone is to an outside object, such as your ear. The Dual SIM capability of Huawei G7 Plus phone is ideal for businesses wishing to provide staff with a mobile device that can offer separate numbers and bills for both personal and business use. This smartphone doesn't support fast charging technology.
accelerometer, compass, light, proximity
The specifications above are based on the official data published by the manufacturer, but we also take user reviews into consideration. If you found an error or something lacking in the specifications above for the Huawei G7 Plus, then don't hesitate and signal the problem to us.
Huawei G7 Plus pictures


A good hotel logo shows class. Logoshuffle helps you to create your hotel logo reliably and presents you with reliable logo suggestions for hotels and catering industry. Of course, you can also choose colors, icons and fonts, as well as incorporate your slogan into the logo.
Just like accommodation and service of your hotel, your logo should be optimally exact to your target group. Black and gold seems Glamorous, blue shows security and self-confidence, green stands for nature and life. A red hotel logo on the other hand can give you attention and show more than other color activity. In short: All colors are possible, according to the nature of your hotel or guest house.
That's where the symbols and icons come into play. Logoshuffle allows you to choose your own icons to pinpoint the meaning of your logo. And that's all about when creating a perfect hotel logo.


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Simon & Schuster Pimsleur Premium is for anyone who enjoys the audio-focused Pimsleur method of learning a language, but also wants interactive exercises to review.
Excellent, well researched learning method. Very well structured. Can export MP3 files and load on a mobile device.
Only available in French, Spanish, German, Italian. Requires broadband connection. Online chat session not offered often enough.
Pimsleur Unlimited edition brings much needed interactive features to this well-known language-learning program, but it still needs to make a few more leaps to fully catch up to the digital era.
The Pimsleur language-learning program has been around for decades in the form of audio tapes, then CDs, and now MP3 downloads. The content is rock solid, but in terms of interactivity, the main program hasn't kept pace with other, newer language apps and software. With Pimsleur Premium for iOS, Android, and Amazon Alexa, Pimsleur takes a step toward changing that. The new package starts with the same audio lessons as before, and adds flashcards, quizzes, and other interactive elements. Pimsleur Premium's only available for a handful of languages, and it's more expensive than the audio-only versions. But if you like the Pimsleur method of learning and want to be able to study on the go, Pimsleur Premium delivers.
Even with the new interactive components, Pimsleur remains heavily audio focused. If that's not for you, try instead Rosetta Stone or Duolingo, our Editors' Choices for paid and free language-learning apps.
Pimsleur Premium is available in eight languages: Mandarin Chinese, French, German, Italian, Japanese, Brazilian Portuguese, Russian, and Latin American Spanish. There's also an English program for Spanish speakers.
The audio-only versions of Pimsleur cover 50 languages. See the full review of Pimsleur Comprehensive for more details.
The Premium package costs $150 per level or $575 for five levels. One level contains 30 lessons of 30 minutes each. You can buy it as an in-app purchase, or you can get a physical software package on disc through Pimsleur's website. The price is the same either way, and it's on the high side for language learning apps.
What Is the Pimsleur Method?
Pimsleur is named for Dr. Paul Pimsleur, an applied linguist who spent years researching how long students remember new information and how often they need to be reminded of it to get it to stick in their longer term memory. He died in 1976, but managed to create a unique language-learning program that lives on to this day.
The program itself has extremely clear instructions. Each day, you're supposed to complete exactly one lesson. The next day, you do the next lesson in consecutive order. If you feel like you didn't master at least 80 percent of the lesson, you're supposed to repeat it the following day instead of moving forward.
No matter what language you choose, the program consists of an English-speaking instructor, plus one or more native speakers of the language you're learning. Only the native speakers use the foreign language. The English-speaking instructor never uses foreign words, but he prompts you and guides you throughout.
The secret sauce is in the intervals. In between learning a new word for the first time and being asked to recall it again, you learn other words and phrases. You're constantly recalling words and phrases that you learned earlier in the current lesson, as well as in past lessons. As you progress, a few days might go by when seemingly out of the blue the narrator will ask, "How do you say, 'I would like?'" and you have to pull it from memory, even if you haven't said it in a while.
It takes maybe five or six lessons to truly get into the swing of Pimsleur. Once you learn how it works, you trust that vocabulary and concepts will repeat a few times, so it's okay if you don't nail it on the first go-around.
What's New in Pimsleur Premium?
So far, the program I've described applies to all the Pimsleur products. The new Pimsleur Premium adds interactive exercises that aren't available in other versions.
In all likelihood, you'll access Pimsleur Premium through a mobile app called "Pimsleur - Language Learning" for Android or iOS. Pay attention to the exact name of the app because there are other Pimsleur apps in both app stores.
In the app, you download audio lessons for the package you've purchased. It keeps track of what you've downloaded, notes which lessons you've played to completion, and saves your place if you start a lesson and are unable to complete it. You can skip ahead if you have some prior experience with the language and the lessons are too easy. Fluenz is another program that lets you jump around; Duolingo, by contrast requires that you test out of levels to skip them.
While playing an audio lesson, you can leave the screen active to see the total time elapsed and have easy access to buttons for pausing/resuming, and backing up or moving forward in 10-second intervals. There's a driving mode that makes these buttons bigger and therefore even easier to see and press. If you prefer to lock your screen, the audio will keep playing.
Another way to do your language learning courses is through the Alexa skill for Pimsleur, if you own an Amazon Echo or other Alexa-enabled product. I didn't test this version, so I can't speak to its ease of use.
For each lesson, you get some combination of these exercises: Reading, Flash Cards, Quick Match, Speak Easy, Speed Round. You're supposed to listen to the primary audio lesson first and then use the exercises to review what you've learned.
Reading contains a list of sounds, words, and expressions you learned in the lesson in a list. You play an audio file of each sound while simultaneously reading it. In Mandarin, you see the pinyin only alongside the audio file. Then, you can toggle to a new screen that shows the Chinese characters, pinyin, and English translation for each entry, too.
Flash Cards let you review the same vocabulary you learned in the lesson. They're self-paced and self-scored. You mark whether you know a word without having to prove it. For Mandarin Chinese, you see pinyin (Romanization of Mandarin) and English only, not Chinese characters. In other places, you do see Chinese characters, however.
Quick Match is a multiple choice exercise where you choose the correct translation from a list of options.
In Speak Easy, you listen to a short dialogue and then repeat it while playing the part of one of the speakers. Again, it's self-paced and self-scored. There's no system that records your speaking and decides whether you're right or wrong.
Speed Round is a game in which words or phrases fall from the top of the screen to the bottom, and you have to find their matching translations and select them before the falling words hit the bottom.
Overall, these exercises didn't challenge my ability to recall words or practice them in an effective way. Considering the structure of the audio lessons—every lesson starts and ends with a dialogue between two people, and you spend the lesson breaking it down—I can imagine other ways to leverage the content into a more challenging interactive lessons. For example, you might have a question at the top of an exercise with multiple choices below, and you have to choose the response that appropriately answers the question. So the question might be, "Do you speak Mandarin?" and the options to answer it could be, "Yes, I speak a little," "Fine thanks, and you?" or "Excuse me, can I ask…?" That way, you have to trigger your memory to recall both the prompt and the possible answers.
In addition to exercises, each lesson also comes with a section called Skills. The Skills are locked until you've listened to the lesson that goes with them, although I find them a little disappointing.
The content of the Skills varies based on the lesson. They're themed to match whatever you've been learning, such as General Phrases, Time, Food, and Numbers. They're really just a list of expressions that you learned in the lesson that you can now review at your own pace. Open any Skill, and you see the list of expressions that fit under that theme from the lesson you just learned. They're written in the foreign language (Chinese uses both pinyin and characters here) with the English translation below. An audio icon indicates you play each one to hear it again.
I wish the Skills offered a new way to think about the content, either with different multiple choice exercises or some other memory challenge, like a fill-in-the-blank exercise.
Should You Busy Pimsleur Premium?
If you like learning with Pimsleur, and you want to be able to refresh your memory about what you learned more often than only when you do your daily lesson, then Pimsleur Premium is worth buying. The price is on the high end for language-learning apps, but if the audio-based style suits you, it may be worthwhile.
That said, there's no reason you can't buy Pimsleur's traditional lessons and use a different free app, such as Duolingo, to add an interactive component. What you learn in each app won't align exactly, but if you start from the beginning with both Pimsleur and Duolingo, you'll get an excellent beginner's experience in both places.
If piecing it all together sounds like too much work, give Rosetta Stone a try instead. It's interactive through and through, which is a big reason it earns an Editors' Choice.
Bottom Line: Simon & Schuster Pimsleur Premium is for anyone who enjoys the audio-focused Pimsleur method of learning a language, but also wants interactive exercises to review.
Jill Duffy is a contributing editor, specializing in productivity apps and software, as well as technologies for health and fitness. She writes the weekly Get Organized column, with tips on how to lead a better digital life. Her first book, Get Organized: How to Clean Up Your Messy Digital Life is available for Kindle, iPad, and other digital formats. She is also the creator and author of ProductivityReport.org.


text:
Jacob Aall Bonnevie Bjerknes, född 2 november 1897 i Stockholm, död 7 juli 1975 i Los Angeles, var en norsk-amerikansk meteorolog. Han var son till den norske meteorologen Vilhelm Bjerknes.

Bjerknes tog doktorsgraden vid Kristiania universitet 1924. Han arbetade därefter i en grupp ledd av sin far med cykloners utveckling. De undersökte livscykel från födelseprocessen, dess förlopp och upplösning och de införde bland annat begreppet fronter.

Bjerknes var även meteorologisk rådgivare till Roald Amundsen när denne genomförde sin första överflygning av Arktis i luftskeppet Norge 1926. Han tilldelades Symons Gold Medal 1940 och invaldes som utländsk ledamot av Vetenskapsakademien i Stockholm 1948. År 1960 erhöll Bjerknes erhöll det amerikanska meteorologisamfundets finaste utmärkelse, Carl-Gustaf Rossby-medaljen.

Referenser

Externa länkar
Store Norske leksikon, artikel om Jacob Aall Bonnevie Bjerknes
Biografi av American Geophysical Union (AGU)
Biographie de Jacob Bjerknes av Arnt Eliassen

Norska meteorologer
Amerikanska meteorologer
Mottagare av Symons Gold Medal
Mottagare av Carl-Gustaf Rossby-medaljen
Ledamöter av Kungliga Vetenskapsakademien
Meteorologer under 1900-talet
Födda 1897
Avlidna 1975
Män

redpajama_set_name: RedPajamaWikipedia


text:
UPDATE: 21 Year-Old Dylan Quick Arrested for Stabbing Spree at Lone Star College
A student named Dylan Quick was taken into custody earlier today after going on a stabbing spree at Lone Star College, leaving at least 14 people wounded.
Though it is believed he acted alone, authorities are advising students and area residents to remain cautious in case there's a second suspect.
From CBS:
Quick was reportedly tackled by students and taken into custody on the campus shortly after the incident took place. He has not officially been charged, according to the station.
Just last week, Quick was featured in a blog about how far he had come and "the battles he fought and won," the station reported.
The blog said Quick was born deaf and received a cochlear implant at seven-years-old. The implant was visible as he was escorted into the Harris County Jail Tuesday afternoon.
Read more at CBS.com
A terrible, deeply disturbing situation.
Our thoughts and prayers are with everyone impacted by this senseless violence.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
14 people have been injured in a stabbing spree at Lone Star College.
Details are still scarce, but multiple people have been rushed to area hospitals, and a suspect is reportedly in custody.
Students have been instructed to find shelter and wait out the tense, dangerous situation.
From NBC:
A spokeswoman for North Cypress Medical Center outside Houston said the hospital had taken six stabbing victims who were in stable condition. The Harris County Sheriff's Office said at least 11 people were hurt, including four who were taken to hospitals in helicopters.
The stabbing happened at 11:20 a.m., Lone Star College said in a statement.
"There are multiple injuries and conflicting reports on the total number of victims and severity of injuries. We can confirm that several people have been transported to area hospitals," the statement said.
As you might recall, a separate Lone Star campus was the site of a "gang related" shooting back in January.; three people were injured.
Read more at NBC.com
We'll keep you updated as this story develops…
Criminal Justice, education, Media, Violence


Genting Singapore - Resorts World, Transform!
Genting Singapore - 4Q18 Results Review ~ Game On!
Stock Strategy Singapore - Will The US$200bn T-Bomb Drop?
Genting Singapore - EBITDA Up 27% YoY!
Genting Singapore (GENS SP) - All Systems Go!
Genting Singapore (GENS SP) - 1Q17 Preview ~ Legs To Run Some More?
Genting Singapore - Three days left in Japan's Extraordinary Diet Session?
Genting Singapore (GENS SP) - D/G to SELL; Rally over done.
Genting Singapore - Luck Still Yet To Turn.
DBS Vickers 2015-08-14: Genting Singapore - Genting Singapore - 2Q15; Out of luck again. Maintain HOLD.
Maybank Kim Eng 2015-08-14: Genting Singapore - Genting Singapore - Poor 2Q but Worthwhile Bet; U/G to BUY.
OCBC Securities 2015-08-14: Genting Singapore - Genting Singapore - HOLD with lower S$0.81 fair value.
RHB Securities 2015-08-14: Genting Singapore - Genting Singapore - Opportunistic Buying On Weakness. Upgrade to TRADING BUY.
UOB Kay Hian 2015-08-14: Genting Singapore - Genting Singapore - 2Q15; Down, But Not Out. Maintain BUY.
CIMB Securities 2015-08-13: Genting Singapore - Genting Singapore - 2Q15; Cheap valuation, but for a reason. Maintain HOLD.
Maybank Kim Eng Research 2015-07-24: Genting Singapore - Genting Singapore - Signs of stabilisation from MBS. Maintain HOLD.


text:
This Is How Much Money Matthew Lewis Is Actually Worth
By Desirée O/Jan. 16, 2020 3:52 pm EST
The cast of Harry Potter may have moved on to different projects, but most surely still have some of the money that they earned while working on the film franchise. Take Matthew Lewis, who played Hogwarts student Neville Longbottom and is now a gorgeous, married, and wealthy man. Lewis is currently sitting on a fortune that's estimated to be around $10 million, according to CelebrityNetWorth. Of course, not all of that money came from his Harry Potter work. Lewis has taken on plenty of other Hollywood gigs that have helped him build his impressive fortune.
CelebrityNetWorth notes that Lewis "has been acting since he was five years old" when he "started off with minor parts in television programs." From there, he auditioned for the Harry Potter series when he was 11, and ended up a part of movie history. And while he surely could have taken the funds he earned from the films and used it to pursue another career (or invest his fortune and never have to work again), he instead has continued to take on new gigs — and earn more money. Fans can catch him in TV series like The Syndicate, Bluestone 42, Happy Valley, Ripper Street, and Girlfriends, just to mention a few.
While it's clear that Lewis has a strong work ethic, he may want to transfer some of that responsibility over to taking care of his money so that he doesn't end up losing it... again.
Matthew Lewis isn't always careful with his money
Frazer Harrison/Getty Images
Matthew Lewis may have a lot of money, but he's not always been careful with it. In 2019, the former Harry Potter actor lost his wallet, which contained cash, credit cards, and something else that was even more valuable.
"Yo, if you stole my wallet in East London yesterday or even if you just found it: it's yours, keep it, have the money, the cards, the lot," the star tweeted on January 22. "But the note from my wife engraved on a piece of metal, if you can post that to the address on the driving licence I'd call it evens. Please?" Lewis married lifestyle and travel blogger Angela Jones back in the spring of 2018, and is obviously fond of the sentimental treasure that she gifted him. Thankfully for the actor, his missing items were returned.
On January 25, just a few days after announcing that his wallet was gone, he again took to Twitter to share, "Wow. You guys are dope. Really humbled by this response... And guess what I have? My wallet! I did not expect that to happen. I owe you all a debt of gratitude and can't thank you all enough. You're amazing. This is a good day." While he didn't reveal how he got his wallet back or indicate if the engraving was also returned, we have to assume so, since his social media message likely would have mentioned if it was still M.I.A.


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Russian court: Telegram app must cooperate with spy agency
Russia's top court ruled Tuesday that the popular Telegram messaging app can be forced to provide user data to Russian security services.
It's the latest blow to the app, which encrypts user communications and has faced pressure from Russian and other authorities in the past.
The Russian Supreme Court threw out an appeal by Telegram protesting demands from the Federal Security Service intelligence agency, or FSB, to provide access to user data.
Telegram argued that the FSB violated consumer rights when it demanded that social networks provide authorities with encryption keys and chat histories.
China blocked Telegram in 2015, and authorities in several countries say Telegram is the message service of choice among Islamic State extremists.
The FSB said the app was used by a suicide bomber who killed 15 people in St. Petersburg last year. French authorities said it was used by IS radicals who killed a priest in Normandy. And Spanish police said this week the man suspected of plotting an IS-inspired attack in Colombia sent suspicious messages on Telegram.
Yet the app is also popular among ordinary people around the world — from Russian election observers to French President Emmanuel Macron's staff. Telegram has claimed it has more than 100 million users.
Following Tuesday's court ruling, Russia's communications regulator ordered Telegram to provide the encryption keys within 15 days. The app could eventually be blocked in Russia if it doesn't comply.
Telegram founder Pavel Durov tweeted: "Threats to block Telegram unless it gives up private data of its users won't bear fruit. Telegram will stand for freedom and privacy."
A ban may be impossible to enforce anyway. When Telegram faced threats of shutdown in the past, it developed an updated version of the app that allows users to bypass an eventual ban by using a virtual private network, or VPN.
Russia adopted counter-terrorism legislation in 2016 obliging communications companies to store call logs and data for months, and to store it in local servers instead of abroad.
The FSB is not asking to see user messages directly, but encryption keys — technical details that would allow security agents to access electronic messages shared through the app if authorities have reason to suspect a threat.
Privacy defenders warn that could give authorities broad range to crack down on dissent.
Telegram, based in Britain, was under threat of closure in Russia last year. Authorities backed off when Durov agreed to register the company in Russia.
Communications Minister Nikolai Nikiforov said Tuesday there's no reason Telegram should be exempt from rules applied to other messaging apps, according to Russian news agencies.


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