Math Calculus Rates (mathematics)
The volume of a growing spherical cell is V = \frac{4}{3} \pi r^3 , where the radius is...
The volume of a growing spherical cell is {eq}V = \frac{4}{3} \pi r^3 {/eq}, where the radius is measured in micrometers. Find the average rate of change of {eq}V {/eq} with respect to {eq}r {/eq} when {eq}r {/eq} changes from
(i) 3 to 6 micrometers
(ii) 3 to 4 micrometers
(iii) 3 to 3.1 micrometers
Average Rate of Change:
Suppose, we have a function {eq}y = f(x) {/eq} and we want to find the average rate of change of this function from {eq}x = a {/eq} to {eq}x = b {/eq}
Then, the average rate of change is:
{eq}f_{avg} = \frac{f(b) - f(a)}{b-a} {/eq}
The volume function of a growing spherical cell is given by:
{eq}V(r) = \frac{4}{3} \pi r^3 {/eq}
Where {eq}r {/eq} is the radius of the spherical...
Average Rate of Change: Definition, Formula & Examples
Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.
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Calculating & Interpreting a Function's Average Rate of Change
The average rate of change in a given function is helpful to identify speeds and other changing variables. Learn why these are used, and how they are calculated and interpreted through examples.
Slopes and Rate of Change
The rate of change is shown through one variable as it changes the function of another variable and can be seen furthermore as location changes as a function of time. Learn more about slopes, rates of change, and the rate of velocity.
Velocity and the Rate of Change
The rate of change refers to how one variable changes based on another variable. Learn about velocity and rate of change by reading an example of the velocity of my drive to work. Then, learn about velocity and inconstant slopes.
Determine the Rate of Change of a Function
The rate of change of a function can refer to how quickly it increases or that it maintains a constant speed. Learn the definitions of linear rates of change and exponential rates of change and how to identify the two types of functions on a graph.
Finding Constant and Average Rates
In mathematics, a rate refers to a quantity, measure, or frequency that something occurs. Learn about finding constant and average rates by using the distance formula through examples.
Data Mining: Identifying Functions From Derivative Graphs
The derivative of a function is the slope of the tangent of the function and depends on it's positive or negative increase to determine it's final state. Learn more about data mining and identifying the functions from derivate graphs.
Rate of Change vs. Negative Rate of Change
Rates of change show how fast a parameter changes with respect to another reference parameter. Learn about rates of change, how to graph rates of change, and see the difference between positive and negative rates of change.
Average and Instantaneous Rates of Change
Rates of change such as acceleration can be measured as average (over a period of time), or instantaneous (single point of time). See how to calculate these two types of rates of change using graphs and calculus.
Solving a Trigonometric Equation Graphically
A trigonometric equation can be solved graphically by providing a visual demonstration of the mathematical answers. Learn how to find the answers graphically and understand what to watch out for when solving trigonometric equations.
Finding Slant Asymptotes of Rational Functions
Learn about slant asymptotes, what they look like, and the rules to calculate them. Understand how to find a slant asymptote with different examples provided.
How to Solve an Absolute Value Equation
An absolute value equation includes a variable that is an absolute value as one of the variables resulting in two solutions, the positive or negative. Learn about the methods of solving basic absolute value equations and why it is necessary to split an absolute value equation into two possible equations to solve for the variable.
What is a System of Equations?
Math word problems often ask students to compare and contrast, which are types of problems that can be solved with a system of equations. Learn about solving word problems using systems of equations and how to graph them, as well as the algebraic method of substitution through an example.
What Are Monomials & Polynomials?
Monomials are constructed of one term of coefficients and variables, whereas polynomials involve two or more terms. Learn from examples of each and discover the significance of the degree of terms.
Methods of Depreciation
When completing financial reports, depreciation, or a loss in value, can be reported using three different methods: straight-line, double declining balance, and units of production. Learn to calculate depreciation using each of these methods.
Zero Product Property Example | What is the Zero Product Property?
What is the zero product property? Learn the zero product property definition and formula as well as how to use the zero product property with examples.
Horizontal and Vertical Asymptotes
Horizontal and vertical asymptotes on a graph reveal points close to the x and y axes that run on infinitely. Learn more about asymptotes, define horizontal and vertical asymptotes, and understand how asymptotes are comparable to an unreachable finish line.
System of Equations Word Problems & Explanations | How to Solve System of Equations Word Problems
Learn how to solve systems of equations word problems. Discover how solving systems of equations word problems is done using the elimination method and the substitution method.
How to Evaluate a Polynomial in Function Notation
A polynomial is an algebraic expression that has more than one term and function notation is the way a function is written. In this lesson, explore how to evaluate or solve a polynomial in function notation.
Introduction to Functions
A mathematical function is a relation between what is input and what is output. Learn more about the purpose of functions, the rules for function and how to write function in notation.
How to Solve a System of Equations by Substitution
Learn all about solving systems of equations by substitution. Understand the steps for how to solve by substitution and see substitution equation examples.
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