Please help

Consider the following function. ((x) = x-2, (a) [5 points] Approximate f by a Taylor polynomial T, (x) with the center x=1. Your answer must be of the form, Co+c, (x-1)+c2 (x-1)2+c;(x-1)3 (b) [5 points] How good is the approximation on the small interval 0.9s xs 1.1? Use the Taylor's Inequality to find an upper bound of the error, IR;(x) |=[/(x)-T3(x)|. (c) [5 points] Find the Taylor series of f(x) with center at x=1. Use the summation notation whoch displays the n-th term clearly. Then, determine the interval of convergence of this series. (d) (Extra Credit 3 points) Show, by using Taylor Ineqality, that the absolute value of the n-th remainder, R,,(x) , converges to 0 for every x in the interval [0.6, 1.4]. (e) (Extra Credit 3 points) Find a rational expression to which this series converges on its interval of convergence. You must show your systematic procedure instead of simply making a wild guess. Hint: Try differentiation or Integration