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MATH152 501 506 Spring 2011 Answers for the sample problems for the Final 1 1 3 2 38 15 3 a 4 15 67 b 2 6 12 5 0 3125 J 4 6 9 2 1 4 7 a 2 5 e 1 x sin 4x C 8 32 1 1 c cos 2x cos 4x C 4 8 3 sec x d C 3 5 1 2 e arcsin x x 5 x C 2 5 b 1 f arctan x C x 2 g ln 3 h 4 8 14 9 145 145 1 81 10 2 11 12 a divergent b convergent but not absolutely convergent 1 c absolutely convergent d convergent 5 7 1 13 radius of convergence R interval of convergence 2 2 2 3 14 e X x 3 n n 0 15 X n 0 n x2n 2 22n 1 2n 1 16 x 1 2 y 2 2 z 32 30 10 17 a arccos 290 10 20 30 40 comp a b b proj a b 29 29 29 29 c a b 9 10 3 18 226 11 19 4 6 20 2
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