1. (a) Prove that e\" 2 1+ 11 for all n E N. (b) Prove that lim (2 + 62") = 2 by using the denition of the limit of a sequence. POO Use the result of (a) in this proof. 2. Consider the function f : ] oo,1[ ) R : x I> f(:1:) = ln(1 x). (3) Find the general expression for f(\"}(:c) with n 2 1. Proof the correctness of this general expression. (b) Provide the Taylor series of f about 0 and determine the convergence radius. (c) Use the Taylor approximation of f about 0 of order 2 to estimate the value of ln(0.5). ((1) Using Taylor's mean value theorem, prove that the error made in (c) is at most