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NHLspl09

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Now although this is a problem for my EE course, it is more of a calculus question so I figured I would receive the best answers by posting it in this section. I have just started on the problem but could use some input on my thoughts. So here we go (there are two parts):

(problem screenshot is attatched)

I'm given the function f(x) = e^ax.

a) Derive an expression for the first three nonzero terms of the Taylor Series for f(x) about x=0 (Maclaurin Series).

b) Complete the following table assuming that a=0.1. The function f(x) is the exact function, the function fts2(x) uses the first two nonzero terms of the Taylor Series, and the function fts3(x) uses the first three nonzero terms of the Taylor Series.

a) Now I know (correct me if wrong) f(x) = f(0) + f ' (0) + ((f ''(0)/2!) x^2) + ... But am not sure if that's the correct answer to the question? Or do I need to take this further?

b) There is then a table with x=0, 0.01, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, & 10. Do I plug these values into the first three nonzero terms found in a? For example, first f(0), then f(0) + f ' (0), then f(0) + f ' (0) + ((f ''(0)/2!) x^2)?

Any help/input would be greatly appreciated!

Thank you

(problem screenshot is attatched)

## Homework Statement

I'm given the function f(x) = e^ax.

a) Derive an expression for the first three nonzero terms of the Taylor Series for f(x) about x=0 (Maclaurin Series).

b) Complete the following table assuming that a=0.1. The function f(x) is the exact function, the function fts2(x) uses the first two nonzero terms of the Taylor Series, and the function fts3(x) uses the first three nonzero terms of the Taylor Series.

## Homework Equations

## The Attempt at a Solution

a) Now I know (correct me if wrong) f(x) = f(0) + f ' (0) + ((f ''(0)/2!) x^2) + ... But am not sure if that's the correct answer to the question? Or do I need to take this further?

b) There is then a table with x=0, 0.01, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, & 10. Do I plug these values into the first three nonzero terms found in a? For example, first f(0), then f(0) + f ' (0), then f(0) + f ' (0) + ((f ''(0)/2!) x^2)?

Any help/input would be greatly appreciated!

Thank you

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