Q4sols

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Unformatted text preview: 1) QUIZ #4 ­ SOLUTIONS Based on the Maclaurin series for sin x , find at least the first four terms of the Maclaurin series for sin x 4 . () x 2 n +1 sin x = ∑ ( −1) ⇒ ( 2n + 1)! n=0 ∞ () sin x 2) 4 n x8n+ 4 1 1 20 1 = ∑ ( −1) = x 4 − x12 + x− x 28 , R = ∞ 6 120 5040 ( 2n + 1)! n=0 ∞ n Based on the Maclaurin series for e x , find at least the first four terms of the Maclaurin series for xe2 x . ∞ xn e =∑ ⇒ n = 0 n! x xe 2 n x n +1 4 =∑ = x + 2x2 + 2x3 + x4 , n! 3 n=0 ∞ 2x R=∞...
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