Note that only problem 1 uses the limit definition. You must find the

derivatives in the other problems using the rules of calculus.

To get maximum credit you must: Write clearly and use correct notation

and units. In particular, make sure you use equal signs and parentheses

correctly. Simplify your answers and explain them with appropriate

reasons, computations, etc. Show all relevant work, not just the final

answers.

If you don't have access to a computer language with mathematical

symbols (such as LaTex), use the ^ symbol for an exponent (e.g., 2^3 =

8), "sqrt" for a square root and "lim(h-->0)" for the phrase "the limit

as h approaches zero." Explain any other symbols you might invent.

1. If f(x) = 1/x2, find f′(x) using the limit definition and show that your result agrees with the power rule.

7+x2

2. Findthetangentlinetothegraphofy= 5−x atx=3.

3. A bug crawls s = ln(1 + t2) inches in t seconds. Find the bug’s velocity when t = 3. √

4. The population of Calculia will number P (t) = 64 + t2 thousand people t years from now. Find the population’s growth rate six years from now.

5. Suppose inverse supply is p = e√q with q measured in tons and p in dollars per ton. Find the elasticity of supply when q = 9.

6. (a) If h = f/g, prove the quotient rule for h′ using logarithmic differentiation.

(b) Rephrase the quotient rule in words (without math symbols) in terms of growth rates.

Subject | Mathematics |

Due By (Pacific Time) | 10/06/2013 12:00 am |

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