Old prac prelim - required 4 Do the problems in any order...

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19,2002 Fe Instructions: 1) Write your name and~our instructor's name on the front cover of the exam booklet (Also put down your section number if you know it) 2) Show all your work. A correct answer will get no credit unless it is clear that your method is correct. 3) Do the problems in any orderyou like, but label the answers clearly. 4) Calculators are not allowed on this test. 1) (15 points) Find a function f and a rn 2) (40 points) { -1-dz; xlnz a) ! dx e) %2-=-4 t) 3) (25 points) a) Evaluate the integral j ~ 0 I ~ A Time: I! hours Math 112, Prelim 1 aber a such that: d) f ~dx cosx g) do1: - .1:'+1
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Sept. 25, 2007 Instructions: 1) Write xour name and xour instructor's name on the front cover of the exam booklet. (Also put down your section number if you know it.) 2) Show all your work. A correct answer may get little credit unless it is clear that you usea correct methodor give an adequate reason. 3) Do not simplify your answers unless
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Unformatted text preview: required. 4) Do the problems in any order you like, but label the answers clearly. 5) This is a closed book test. Calculators, notes, or crib sheets are not allowed. Some of the following cos29 = ~(1 + cos 29) 1) a)(10 points) Find the derivative ofG(x) if G(x) = b)(5 points) Suppose J 2) (30 points) Find the a)! xlnxdx " zS-s d)f 3)(20 points) Let R denote the region bounded by the graphs of, = 2 _,1;2 and y = -2. a) Sketch this region. b) Write an integral representing the area ofR. c) Evaluate the integral you found in part (b). 4) (15 points) Math 112, Prelim 1 Time: 7.30 -9p.m. formulas may be useful: I sin28 = !(l - cos28) tan28 = sec28 - 1 11 etJ dt L' 12, (Try a substitution). J(t) dt = 3. Calculate 1(2t) dt l 1f/2 c) 0 sin2x dx b) f e.fi dx 3/2 e) %+1 4:;2+9 d% whether the following integral converges or diverges: 1 00 coax 0 x2+1 dx...
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