In this problem, you will investigate the error in the nth degree Taylor approximation to ln(x+1) about 0 for various values of n.

Question

(a)Let E_1=ln(x+1)−P_1(x)=ln(x+1)−(x). Using a calculator or computer, graph E1 for −0.1≤x≤0.1, and notice what shape the graph is. Then use the Error Bound for Taylor
polynomials to find a formula for the maximum error,as a function of x, in this case: |E_1(x)|≤?.
(b)Let E_2=ln(x+1)−P_2(x)=ln(x+1)−(x−x^2/2). Choose a suitable range and graph E_2 for −0.1≤x≤0.1. Again, notice what shape the graph of E_2 is. Then use the Error Bound for Taylor polynomials to find a formula for the maximum error, as a function of x, in this case: |E_2(x)|≤?.