Written Assignment #3 Math 120 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 mean, Appropriate grammar and punctuation!) and should include a full, claw aplane- tion. Do not use a calculator (physical or online) unless explicitly asked to. Context: For much of this written assignment, we will explore various use of Taylor polynomials. You may take for granted the following: Given a function / : 1 - R and its Taylor polynomial 3, amended around a 1, it is a fact that there is c in between 1 and I such that (or + 1)! (B) Here flatl) is the (or + 1)th derivative of f, and recall that ( (0) 2 You may recognise the m 0 case as the "Mean Value Theorem."Problem 1. (?) Using (E) with n 1 and f(a) In(1+ x), show that In(1+y) Ky breweryy 2 0. (2) Using (E) with n 2 and f(a) Io(1+ 1), show that "{lo(lty) for everyy 2 4. 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 > > ( then ( 8 c g s, and if :