sol for exam 2 take home

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online