Math Pre-Calculus Limits of functions
Is the function h(x) = 3x + 2 for x less than 4 and 18-x for x greater than 4 continuous at the...
Is the function {eq}h(x)=\left\{\begin{matrix} 3x+2 & \mathrm{for}\;x<4\\ 18-x & \mathrm{for}\; x > 4 \end{matrix}\right. {/eq} continuous at the point {eq}x = 4 {/eq}?
Continuous function:
A trivial definition of a continuous function is that If the graph that defines the function can be traced without lifting the finger from the paper, that is, if the function can be traced with a single stroke, then it is continuous.
Given the function
$$\begin{align} h(x)=\left\{\begin{matrix} 3x+2 & \mathrm{for}\; x<4\\ 18-x & \mathrm{for}\; x >...
How to Determine if a Limit Does Not Exist
Chapter 4 / Lesson 9
Determining if a limit does not exist requires information about the limit type, its asymptote, and graphed point. Study the formulas associated with finding these metrics and how they are used to determine whether right-hand, left-hand, or two-sided limits exist for a function.
Find the lim as h approaches 0 of (sqrt(16 + h)...
Evaluate the limit. lim (as h goes towards 0)...
Find the limit: lim h to 0 1 - 1/h^2/1 -...
Evaluate the limit, if it exists. a) limit h...
Show by means of an example that lim x ->a...
Find the limit of e^{2t} i + {sin(4t)/4t} j...
If \lim\limits_{x \rightarrow 2} (f (x) + g(x))...
If \lim\limits_{x \rightarrow 2} (f(x)+g(x ))...
Consider the function f(x) = ((x - 1)^3)/((x +...
Find lim_{x to infinity}...
Analytically, find lim_{x to infinity}...
Evaluate the limit. Limit_{x to 2}...
Evaluate the limit. Limit_{x to -2}...
solve { lim _{x \to 0} \frac{(1+sinx)^{1/3} -...
Evaluate the limit. Limit_{x to 2} Limit_{x to...
Evaluate the limit. \lim_{t\rightarrow...
Find \lim_{x\rightarrow \infty}...
Evaluate L = \lim\limits_{x \rightarrow \infty}...
Using a Graph to Define Limits
Limits can be visualized and defined better with the use of graphs. Explore examples of limits defined by graphs such as speed limits and limits of a pendulum, as well as other limits in math.
Regions of Continuity in a Function
A region of continuity is where you have a function that is continuous and is a critical understanding in calculus and mathematics. Learn more about regions of continuity as a function and read examples.
Undefined Limits: Definition & Examples
An undefined limit occurs when a function does not approach a finite value. Learn the definition and examples of undefined limits, one-sided limits, infinite oscillations, and endpoint intervals.
How to Find Limits Using Asymptotes
The limits of a polynomial function can be determined by using the asymptotes of the function. Learn about the relationship of limits and asymptotes, and take a look at the steps in finding the limits of a function using the given asymptotes of the function.
Concavity and Inflection Points on Graphs
Inflection points and concavity give graphs their smooth sloped shape, like a skateboarding ramp. Learn how to define concavity and concave up/concave down lines as well as how to identify the inflection points of concave lines.
Limits with Absolute Value
Absolute value is a measure of how far away a positive or negative number is from zero and it is used to find limits in functions. Learn how absolute value and limits work, with examples of functions without limits, one-sided limits, and the piecewise function.
Jump Discontinuities: Definition & Concept
Jump discontinuity is a classification of discontinuities in which the function jumps, or steps, from one point to another along the curve of the function, often splitting the curve into two separate sections. Learn about piecewise functions and how to check for jump discontinuities in a function.
Understanding the Properties of Limits
The key to understanding the properties of limits is that it requires dividing the function into its individual parts first. Learn more about the properties of limits, including the addition and subtraction property, product property, and division property.
Intermediate Value Theorem: Definition
The intermediate value theorem concerns the properties of continuous functions over a range and finding at least one solution. Learn more about the definition of the intermediate value theorem using the altitudes of a jet airplane as an example.
Approximating Limits on a Graphing Calculator
A graphing calculator has a built-in function that approximates the limits of a function based on an equation and its graph. Learn about the steps by using the TI-84 graphing calculator and how to use the TRACE command for graphing.
Testing for Convergence & Divergence by Comparing Series
Discover how to test for convergence and divergence in a series by comparing it to another series. Examine more about comparing series, explore how to test for convergence and divergence, and take a look at an example.
Calculating Derivatives of Polynomial Equations
Derivatives of polynomial functions can be solved in a simpler way by using the power rule for derivates. See how this rule can be used to solve vertical velocity functions, and how to find derivatives of polynomials through examples of the steps involved.
What is the Addition Rule for Limits? - Definition & Overview
In this lesson, you will learn how to identify problems in which you can apply the addition rule for limits. You will also learn in what instances you cannot use this very helpful rule.
Removable Discontinuities: Definition & Concept
Removable discontinuities are points in a graph that are undefined or do not fit the rest of the graph. Understand the concept of removable discontinuity, how it is formed, and how to find holes.
How to Find Critical Points of a Function
In this lesson, learn what critical numbers of functions are and how to find the critical points of a function. Moreover, see examples of critical points on a graph for a better understanding of what they represent.
Continuity in Calculus Examples | Rules & Conditions of Continuity in Calculus
What is continuity in calculus? Learn to define "continuity" and describe discontinuity in calculus. Learn the rules and conditions of continuity. See examples.
Finding Asymptotes Using Limits
The asymptotes of a function can be determined based on the limits of the given function. Learn about the different types of asymptotes and how to find the asymptotes of a given polynomial function.
How to Determine the Limits of Functions
A limit can tell us the value that a function approaches as that function's inputs get closer and closer to a number. Learn more about how to determine the limits of functions, properties of limits and read examples.
Squeeze Theorem Limits, Uses & Examples | What is the Squeeze Theorem?
In this lesson, learn the definition of the squeeze theorem and discover squeeze theorem examples. Moreover, learn how to use the squeeze theorem.
Discontinuous Functions | Properties & Examples
What is a discontinuous function? Explore discontinuous function examples and learn when is a function discontinuous and how to find discontinuity of a function.
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