137p_Assignment4.pdf - MATH 137 Winter 2020 u2013...

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MATH 137 Winter 2020 – Assignment 4Due: 5 pm Friday, March 27.1. Determine the first three non-zero terms in the Maclaurin series for the following.a)sinxx(x >0)b)ex1-xc) ln1 +x1-xDetermine the first three non-zero terms of the Taylor series for the following functions about the given points.d)f(x) =1x,x0= 1,e)f(x) = sinx,x0=π62. Compute the value ofd3dx3x2ex1-xatx= 03. Evaluate the following limits using Maclaurin series.a) limx0sinx-xx3b) limx0ln (1 +x)x2-1xc) limx01-ex3xln(1-x2)4.Define the functionf(x) =x/(ex-1) so thatf(0) = 1, then the Maclaurin expansion off(x) has a positiveradius of convergence.

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