Question 5 (12 marks) a. Show that the first four terms of the Taylor series for f (x) =e"* about x =0 are X f ( x) =1-x+ + . . 2! 3! (4 marks) b. Use the first three terms of the Taylor series to estimate the value of er, that is, the value of e"* when x=0.1. (2 marks) c. Find an absolute bound on the error of your estimate for ed from part b. (4 marks) d. Use the exponential function on your calculator to find ed exactly and calculate the true error in your estimate from part b. Comment on whether the true error is consistent with the error bound from part c. (2 marks)