sol for exam 2 take home

# Kx ln k2 agree that f x can be written as 1 lim ln

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Unformatted text preview: − ∞ → 1+ x 2 1− x 2 x 3 1+ ··· · 1+ x n 1− 1− x n x 3 · . ⋆ Just check the box ‘Agreed’. (1b) Agree that g x can be written as n 1 1 lim − x+ ln k 2 n− ∞ → k=2 1+ x 2 1− x 2 ⋆ Just check the box ‘Agreed’. 4 1+ x 3 · ··· · 1 + x n 1− x 3 · ··· · 1 − x n . (2a) Give the Taylor series expression of −f x Answer for (2a) ∞ m=2 −1 ζm −1 m 2 ζ −1 x 3 ζ −1 + x 5 −1 x 5 6 ζ 5 − −1 x ζ 3 − 3 + 6 6 4 −1 x 4 + ··· . : Work for (2a) −f x 2 xm 2 ζ . : m−1 =− +gx +gx = lim − n− ∞ → n k=2 = lim − n− ∞ → n k=2 1 x x + ln 1 + k 2 1 x+ k n ln 1+ k=2 5 1+ x k x 3 · ··· · 1+ x n 4 = n 1 lim − x+ k n− ∞ → k=2 n = lim n− ∞ → k=2 n = lim n− ∞ k=2 ∞ ∞ = k=2 − ∞ = x k x k − −1 −1 k=2 + ∞ m=2 −1 ∞ = m=2 −1 m−1 −1 x k −1 + m m=2 m m m−1 m x k m−1 ∞ x k m−1 m m=1 m−1 m x k m x k m−1 m x k two Σs were interchanged 1 km k=2 x m m−1 −1 ∞ m=1 ∞ = + m k=2 n ∞ m m=2 ∞ m=2 ζm −1 m xm . 6 m (2b) Give the Taylor series...
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## This note was uploaded on 01/12/2014 for the course MATH 116 taught by Professor Scholle,minho during the Fall '08 term at Kansas.

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