# old final - Problem 2 (9 points) Find T and N for the curve...

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Math 2401 Final Open Book and Notes. Carefully explain your proceedures and answers. Calculators allowed, but answers mush be exact. Problem 1 (10 points) Find the surface integral ± ± curl F ± n ²Σ , over the surface S, which is given by z = x 2 + y 2 , 0 £ z £ 2. Here F = I x 3 y 2 M i + xy 2 j + x z k . Set this up as a surface integral and convert to an ordinary double integral. Then use Stokes’ s Theorem to convert to line integral H s L . Convert these line integral H s L to ordinary one variable integral H s L . The surface S does not include the top of the cone. The normal is the one illustrated ± Ans ±

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Unformatted text preview: Problem 2 (9 points) Find T and N for the curve x(t) = cos(t), y = sin(t), z = t 3 Ans Final Spring 2007 Tom Morley 8:00 am Problem 3 (10 points) Find the area of the cardiod r= (1-cos( )) that is above the curve y = |x| (absolute value). Ans Problem 4 (9 points) Find the the box of minumum cost constructed WITHOUT TOP if the cardboard for the sides is 2 cents a square foot,, and the cardboard for the bottom is 8 cents a square foot. The box is to have a total volume of 64 square feet. Ans 2 final2007.nb...
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## This note was uploaded on 06/07/2009 for the course MATH 2401 taught by Professor Morley during the Spring '08 term at Georgia Institute of Technology.

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old final - Problem 2 (9 points) Find T and N for the curve...

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