This problem asks for Taylor polynomials for f(x) = ln(1 + x) centered at a = 0. Show your work in an organized way. (a) Find the 4th, 5th and 6th degree Taylor polynomials for f(x) centered a = 0.

(b) Find the nth degree Taylor polynomial for f(x) centered a = 0, written in expanded form.

(c) Find the nth degree Taylor polynomial for f(x) centered a = 0, written in summation notation.

(d) Use the 7th degree Taylor polynomial to estimate ln(2).

(e) Compare your answer to the estimate for ln(2) given by your calculator. How accurate were you?

(f) Looking at the Taylor polynomials, explain why this estimate is less accurate than the estimate in the previous problem for sin(3? ).