Chapter 2: Q 38 (page 238)
If ,find
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Instead of choosing small values of h, we could have chosen values of z close to c. What limit involving z instead of h is equivalent to the one involving h?
Differentiate in three ways. When you have completed all three parts, show that your three answers are the same:
(a) with the chain rule
(b) with the product rule but not the chain rule
(c) without the chain or product rules.
State the chain rule for differentiating a composition of two functions expressed
(a) in “prime” notation and
(b) in Leibniz notation.
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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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