quiz xxx solutions

# quiz xxx solutions - Math 116 CALCULUS II SOLUTION FOR QUIZ...

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Math 116 CALCULUS II SOLUTION FOR QUIZ – XXX (12/03) December 3 (Tue), 2013 Instructor: Yasuyuki Kachi Line #: 23590. [I] (8pts) Find the following special values: (1) sin 0 = 0, (5) cos π 2 = 0. (2) sin π 6 = 1 2 . (6) sin 2 π 3 = 3 2 . (3) cos π 4 = 1 2 . (7) sin π = 0. (4) sin π 3 = 3 2 . (8) cos p 2 π P = 1. [II] (2pts) p cos x P 2 + p sin x P 2 = 1. [III] (4pts) (1) sin p - x P = - sin x . (2) cos p π 2 - x P = sin x . (3) sin p π - x P = sin x . (4) cos p 2 π + x P = cos x . [IV] (10pts) d dx p sin x P = cos x . d dx p cos x P = - sin x . 1

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The Taylor series for sin x : sin x = s n =0 p - 1 P n p 2 n + 1 P ! x 2 n +1 = x - 1 3 ! x 3 + 1 5 ! x 5 - 1 7 ! x 7 + 1 9 ! x 9 - ··· . The radius of convergence
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