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Math 16B: Homework 5 Solutions

Math 16B: Homework 5 Solutions Due: July 30 1. Find the nth Taylor polynomial for each of the following functions at the given point: (a) n = 2: f(x) = x1=3 at x = 27: We have f′(x) = 1 3x2=3 and f ′′(x) = −2 9x5=3.Since f(27) = 3, f ′(27) = 1 27 and f′′(27) = −2 2187, the 2nd Taylor polynomial of f centered at x = 27 is P(x) = 3+ (127) 1 (x 27)+(−22187) 2 (x 27)2= 3+ x 27

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