Chapter 2: Q. 85 (page 199)
Use thedefinition of the derivative to prove the power rule holds for positive integers powers
Short Answer
We prove the power rule holds for positive integers powers using the definition of derivative
Chapter 2: Q. 85 (page 199)
Use thedefinition of the derivative to prove the power rule holds for positive integers powers
We prove the power rule holds for positive integers powers using the definition of derivative
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Get started for freeDifferentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
28.
For each function f and value in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
Use the definition of the derivative to find for each function in Exercises 34-59
The total yearly expenditures by public colleges and universities from 1990 to 2000 can be modeled by the function , where expenditures are measured in billions of dollars and time is measured in years since 1990.
(a) Estimate the total yearly expenditures by these colleges and universities in 1995.
(b) Compute the average rate of change in yearly expenditures between 1990 and 2000.
(c) Compute the average rate of change in yearly expenditures between 1995 and 1996.
(d) Estimate the rate at which yearly expenditures of public colleges and universities were increasing in 1995.
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