Calculus for Life and Social Sciences I, summer 2004
Calculus for Life and Social Sciences II
Summer 2005
Exam #3 Name___________________
This exam is close book, close notes and close neighbors. Show all your work to receive full and/or partial credits. You are allowed to use a calculator and one page note ([pic]). Please note that point values are given in the margin.
1. Use L’hospital’s rule to find the limit. [pic]
2. Evaluate the improper integral
[pic]
3. Find [pic] and [pic]for the function [pic]
[pic]
[pic]
4. A cargo container (in the shape of a rectangular solid) must have a volume of 480 cubic feet. Use Lagrange Multipliers to find the dimension of the container of this size that has a minimum cost, if the bottom will cost $5 per square foot to construct and the sides and top will cost $3 per square foot to construct.
[pic]
Constraint [pic]
[pic]
[pic] [pic]
[pic]
[pic][pic]
5. Find the critical numbers and use second partial tests to determine the relative extrema for the function[pic]. You must show all the necessary partial derivatives.
[pic] [pic]
[pic] Relative max at (8, 16, 74)
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