Given a function f : R - R and its Taylor polynomial Pn expanded around a =0, it is a fact that there is c in between' ( and I such that (n + 1)! (E) Here f(+1) is the (n + lith derivative of f, and recall that -2 fm) (0) + . . . + k! k - 0 2 You may recognize the n = 0 case as the "Mean Value Theorem." Problem 1. (i) Using (E) with n = 1 and f() = In(1 + 2), show that In(1 ty) Q. (ii) Using (E) with n = 2 and f () = In(1 + 2), show that 3 - 0.(ini) Use (i) and (ii) to deduce that, for every z ( [0, 1], 2