(a) Find the Taylor series for f(x) = et centered at a = 1 and its radius of convergence. f (n ) : ex , f ( 1 ) = else Let on = ( 7 - 1 )" f) (x) =e" , f ( 1 ) = else g anti-- ( n+1) ! n ! an lim Ju-1 = 051 21 Taylorseries - 3 Jager / Hence + ( the radily (b) Find the Taylor polynomials up to degree 4 for f() = er centered at a = 1. Graph f and wa to LA-I!' of convergence will ntT these polynomials on a common screen. eel x-1 ) ely - 1 ) elm - 1 ) 3 1 1 2 1 3 ! (c) Use Ta(r) to approximate the value of ell. (d) Use Taylor's Inequality Formula to find the error bound when approximationg eld with TA(I). (e) Use Taylor's Inequality Formula to estimate the accuracy of the approximation TA(r) when r lies in the interval [0, 2]. (f) Check your result in part (e) by graphing | RA(x) | for O S I S 2