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) = ln(1 + x) centered at a = 0.
(b) find the nth degree taylor polynomial for f(x) centered at a = 0, written in expanded form.
(c) find the nth degree taylor polynomial for f(x) centered at a = 0, written in sigma (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 you found for sin(3°) in problem 6 of homework 10. (in that problem, you were asked to use a 7th degree taylor polynomial centered at a = 0 for sin(x) to approximate sin(3°