part a,b,c,d,e,f please and thank you

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