SampleFinal133 - Math 133 Final Exam, Spring 2006 Name: _...

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Math 133 Final Exam, Spring 2006 Name: ____________________________ Instructor: ___________________ PID: ______________________________ Section: ___________________ Total: ____________ Instructions: There are 10 pages, with a total of 200 possible points. You must show all necessary work to receive credit. Calculators are not allowed on this exam. ______________________________________________________________________________ 1. Find the derivative for the following functions. (a) (10 points) ( ) 2 1 sin x y = (b) (10 points) . Simplify your answer. () 2 ln 2 4 ln 2 + = x e y
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(c) (10 points) () x x y = . Write dy dx in terms of x only. You do not need to simplify. 2. (9 points) Find the solution of the differential equation sinh dy y x dx = satisfying the condition (0) 1 y = . Solve for y in explicit form. (That is, write y as a function of x.)
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3. Set up, but do not evaluate , the integral for the volume of the solid generated by revolving the finite region bounded by y = x , the x-axis and the line x = 4 (a) (6 points) about the x-axis (Include a rough graph of the rotated solid) (b) (6 points) about the line y = 3 (Include a rough graph of the rotated solid)
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4. (7 points) Set up, but do not evaluate , an integral for the length of the curve 2 x y e = , .
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This note was uploaded on 05/12/2008 for the course MATH 133 taught by Professor Wei during the Spring '07 term at Michigan State University.

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SampleFinal133 - Math 133 Final Exam, Spring 2006 Name: _...

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