Consider the functionf(x)=1/(1x).

a)Enter the degree-nterm in the Maclaurin polynomial.

b)Enter the remainder termRn(z)which will also be a function ofxand n.

c)For negativex,find an upper bound forRn(z)over all values ofzbetween 0 andx.This upper bound will be a function ofxandn.(Hint: the remainder term may be positive or negative depending on the value ofn,to get an upper bound that works for allnyou may need to make sure that your answer is always positive, since this will be an upper bound in either case.

d)Use this upper bound to find how many terms are needed to estimatef(-0.4)with an error term less than10^-8