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The final exam for the applied calculus course offered at rhodes college during the spring 2008 semester. The exam covers topics such as finding derivatives of functions, partial derivatives, integrals, and applying the limit definition of derivatives.
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Rhodes College Math 115: Applied Calculus Final Exam Spring, 2008
Note: SHOW ALL WORK. Answers with no support will receive no credit, even if the answer is correct. May the force be with you.
Have you taken a calculus class in the past?
If you have, what class, where, and when?
2 t^3 + t^2 +2t (Use the quotient rule or equivalent).
x
a. (4 pts) What is the derivative of f (x)?
b. (4 pts) For what values of x is f (x) increasing?
c. (7 pts) Find all local maxima and minima of f (x).
x 4
a. (5 pts) Use a Right Riemann Sum with n = 4 to approximate how much F (x) increases between x = 0 and x = 4.
b. (5 pts) Use a Midpoint Riemann Sum with n = 4 to approximate how much F (x) increases between x = 0 and x = 4
∫^4
2
0
x^2 y + y^2 x dy
(^) dx
