quiz xxx solutions

Iv 10pts d dx sin x d dx cos x 1 cos x sin

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Unformatted text preview: x d dx = cos x. 1 cos x = − sin x. The Taylor series for sin x: n −1 ∞ sin x = n=0 = x− x2n+1 2n + 1 ! 1 x3 + 3! 1 x5 − 5! 1 x7 + 7! 1 x9 − · · · . 9! 1 x6 + 6! 1 x8 − · · · . 8! The radius of convergence R = +∞. The Taylor series for cos x: n ∞ cos x = n=0 = 1− −1 x2 n 2n ! 1 x2 + 2! 1 x4 − 4! The radius of convergence R = +∞. [V] (6pts) (1) sin x+y = sin x cos y + cos x sin y , (2) cos x+y = cos x cos y − sin x sin y . 2...
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