Instructions: Each question will be graded both for correctness and for work shown. The latter is extremely important solutions should be written using proper English (that means, appropriate grammar and punctuation!) and should include a full, clear explana tion, Do not use a calculator (physical or online) unless explicitly asked to. Context: For much of this written assignment, we will explore various uses of Taylor polynomials. You may take for granted the following: Given a function f : R - R and its Taylor polynomial Pr expanded around a = 0, it is a fact that there is c in between' 0 and z such that (n + 1)! (E) Here f(+1) is the (n + 1)th derivative of f, and recall that PR(c) = M: k! 2 n! You may recognize the n = 0 case as the "Mean Value Theorem." Problem 1. (4) Using (E) with n = 1 and f(x) = In(1 + 2), show that In(1 ty) Q. (ii) Using ( E) with n = 2 and f(c) = In(1 + 2), show that 3 - 2