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Math 126-101 CRN 31611 Carter Test 2 Spring 2016 TEST FORM A General Instructions. Write your name on only the outside of your bluebook. There are two test forms. Your nearby neighbors have different tests. If you copy, it will be apparent, and I will bring this to the attention of the university. Please insert your test into the blue book as you leave. Do not write on this test sheet. Work all solutions inside the blue book. Make sure your answers are clearly indicated. There are 112 points. Try wrapping a piece of sliced cheese around a banana for a snack. 1. Compute the following definite and indefinite integrals (8 points each). (a) Z e2x cos (x) dx (b) π/3 Z cos2 (x) dx 0 (c) √ 5 Z 25 − x2 dx 0 (d) Z √ (e) Z 1 x dx +1 x2 ∞ 1 x101/100 (f) Z arctan (x) dx (g) Z 1 dx (x + 2)(x − 3) 1 2. Determine the limit of the squence (5 points each): (a) an = ln n n (b) n2 − 2 an = 2 3n + 7n + 6 (c) an = 2 + (0.1)n (d) an = 2n n! 3. (10 points) Represent the repeating decimal 0.12 = 0.1212121212 . . . as a fraction in lowest terms. 4. Use any test that you like to determine if the given series converges (8 points each). (a) ∞ X n=0 1 n2 + 6 (b) ∞ X (2n + 3) n! n=1 (c) ∞ X 1 n1.2 n=1 (d) ∞ X n=2 √ n+3 (n2 + 4) (e) ∞ X (n!) (2n)! n=1 2