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

## Question:

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

Consider the function f(x) = exp(x) = e^{x}. Suppose we know the value of f(x) at x = x_{0}, i.e., we know the value of f(x_{0}), and we want to estimate the value of this function at some x location near x_{0}. Generate the first four terms of the Taylor series expansion for the given function (up to order dx^{3} as in the above equation). For x_{0} = 0 and dx = –0.1, use your truncated Taylor series expansion to estimate f(x_{0} + dx). Compare your result with the exact value of e^{-0.1}. How many digits of accuracy do you achieve with your truncated Taylor series?

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**Related Book For**

## Fluid Mechanics Fundamentals And Applications

**ISBN:** 9780073380322

3rd Edition

**Authors:** Yunus Cengel, John Cimbala