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(a) Find the Taylor series for f(x) = er centered at a = 1 and its radius of convergence. (b) Find the Taylor polynomials up to degree 4 for f(x) = et centered at a = 1. Graph f and these polynomials on a common screen. (c) Use Ta(I) to approximate the value of ell. (d) Use Taylor's Inequality Formula to find the error bound when approximationg ell with TA(I). (e) Use Taylor's Inequality Formula to estimate the accuracy of the approximation T4(r) when r lies in the interval [0, 2]. (f) Check your result in part (e) by graphing | RA(x) | for 0 S x 5 2