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### calc2_final

Course: MATH 112, Fall 2009
School: NJIT
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112 Final Math Exam December 17, 2004 Read each problem carefully. Please show all your work for each problem! Use only those methods discussed thus far in class. No calculators! 1. (10 points) Compute: (a) lim 1 - cos , 0 22 (b) lim x2 e-2x , x (c) lim (1 + 2x)1/x . x0+ 2. (10 points) Integrate: 2 (a) 0 dx , 16 - x2 (b) x cos 2x dx, (c) sin3 x dx 3. (12 points) Integrate (evaluate the improper...

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112 Final Math Exam December 17, 2004 Read each problem carefully. Please show all your work for each problem! Use only those methods discussed thus far in class. No calculators! 1. (10 points) Compute: (a) lim 1 - cos , 0 22 (b) lim x2 e-2x , x (c) lim (1 + 2x)1/x . x0+ 2. (10 points) Integrate: 2 (a) 0 dx , 16 - x2 (b) x cos 2x dx, (c) sin3 x dx 3. (12 points) Integrate (evaluate the improper integrals correctly): (a) dx , 2 - 3x - 4 x (b) 2x + 1 dx, x2 + 4 (c) 1 dx . x2 4. (12 points) Find the area of the region in polar coordinates lying outside the curve r = 1 and inside r = 2 cos . 5. (10 points) Find the first two non-zero terms in the Maclaurin Series of the function f (x) = arctan x. 6. (10 points) whether Determine the following series converge or diverge. Find the sum of those that converge. Justify your answer! (a) n=1 n, (b) n=0 2n - 3n , 4n (c) n=0 1 . xn 7. (12 points) Determine whether the following positive term series converge or diverge. State clearly which test you use. (a) n=0 n , 4+1 n (b) n=1 2n n! (c) n=1 ln n n 8. (12 points) Determine whether the following series converge absolutely, conv...

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