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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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