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Unformatted text preview: Math 165 Final Exam Part I May 2010 Full Name: TA: Section: Instructions: Part I of the exam consists of 3 pages. Hand in Part I after 40 minutes. Show all work, all steps of calculations, and simplify answers. You may NOT use a calculator. Each part is worth 5 points. 1. Find the following definite integrals. (a) Z 3 1 5 x + 5 x 2 + 2 x + 2 d x (b) Z 1 1 x cos( x 3 ) d x 2. Find the following indefinite integrals. (a) Z x exp( x 2 ) d x (b) Z 1 + 4 ln x x d x Math 165 Final Part I Page 2 3. Find the derivatives of the following functions. (a) h ( x ) = x 3 3 x 2 1 (b) y = ln x √ x 3 (4 x + 5) 10 Math 165 Final Part I Page 3 4. Find the derivative of the function y ( x ) given for 3 < x < 1 by 0 < y < π and cos y = x + 2 . 5. Find that solution of the differential equation d y d x = x 3 √ y which satisfies y = 2 when x = 0. Math 165 Final Part II Page 4 Full Name: TA: Section: Instructions: Part II of the exam consists of 4 pages. Begin after you have finished Part I, but you may only use a calculator after 40 minutes. Show all work. No credit allowed forI, but you may only use a calculator after 40 minutes....
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 Spring '08
 Hotlz
 Math, Calculus, Optimization, following definite integrals, differential equation dy

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