Written Assignment #3 Math 129 Due April 14, 2022, 11:59 pm GRADESCOPE 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 Add, clear explone- 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 polynomid Pre expended around a = 0, it is a fact that there is c in between' 0 and a such that (n + 1)1 (E) Here f(+1) is the (n + 1) th derivative of /, and recall that 103 (0) 2 You may recognize the n = 0 case as the "Mean Value Theorem." Problem 1. (1) Using ( E) with n = 1 and f(@) = In(1 + 2), show that In(1 +y) Cy for every y > Q. (vi) Using (E) withn = 2 and f(@) = In(1 + 2), show that y - 2 Elm(l ty) for everyy 2 0. For an idea of what I mean by this, imagine you show your solution to another student in Math 129 who has not completed the problem. That student should be able to understand each step of your argument based on what you have written on the page. 'By this, we mean that: if i > 0 then O o s, and if I