A Taylor series expansion of function f (x) about some x-location x0 is given as f(x0 1

Chapter 9, Problem 9-9

(choose chapter or problem)

A Taylor series expansion of function f (x) about some x-location x0 is given as f(x0 1 dx) 5 f(x0) 1 a df dxb x5x0 dx 1 1 2! a d2 f dx2 b x5x0 dx2 1 1 3! a d3 f dx3 b x5x0 dx3 1 p Consider the function f (x) 5 exp(x) 5 ex . Suppose we know the value of f (x) at x 5 x0, i.e., we know the value of f (x0), and we want to estimate the value of this function at some x location near x0. Generate the first four terms of the Taylor series expansion for the given function (up to order dx3 as in the above equation). For x0 5 0 and dx 5 20.1, use your truncated Taylor series expansion to estimate f (x0 1 dx). Compare your result with the exact value of e20.1. How many digits of accuracy do you achieve with your truncated Taylor series?