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MATH 105 EXAM 2 November 12, 2004
Name:
While a final answer is important, you earn points for all the work leading to that answer, not just the answer itself. Show all your steps clearly so you will be eligible for the most partial credit. You may use a calculator, but no notes, books, or other students. Good luck!
1.) (10 pts.) For some positive constant C, a patient’s temperature change, T , due to a dose, D, of a drug is given by
T (D) =
( C 2
D
) D^2.
What dosage maximizes the temperature change?
2.) (10 pts.) Compute s′(y) if s(y) = 3
√ (cos^2 y + 3 + sin^2 y). SIMPLIFY COMPLETELY, and remember you can simplify both before and after computing the derivative.
3.) (10 pts.) Compute f ′(z) if f (z) =
5 z + 5
z +
z
√ 5 z
5.) (10 pts.) For x > 0, find and simplify the derivative of f (x) = arctan x + arctan(1/x). What does your result tell you about f?
6.) (10 pts.) Find
dy dx if x^2 + xy − y^3 = xy^2.
7.) (10 pts.) Find the tangent line approximation to (1 + x)^3 /^2 near x = 0.
8.) (10 pts.) Compute the following limits:
a.) lim x→ 2
ex x
b.) (^) xlim→∞ ex x
