- #1

MelissaJL

- 50

- 0

## Homework Statement

Determine the first three terms in the Maclaurin series for:

(x

^{2}+4)

^{-1}

## Homework Equations

f(x)=f(a)+f'(a)(x-a)+f''(a)[itex]\frac{(x-a)^{2}}{2!}[/itex]+f'''(a)[itex]\frac{(x-a)^{3}}{3!}[/itex]

## The Attempt at a Solution

So I start out with getting my primes of f(x):

f'(x)=[itex]\frac{-2x}{(x^{2}+4)^{2}}[/itex]

f''(x)=[itex]\frac{6x^{2}-8}{(x^{2}+4)^{3}}[/itex]

f'''(x)=[itex]\frac{24x(x^{2}-4)}{(x^{2}+4)^{4}}[/itex]

So my issue is that when I set a=0 for the Maclaurin series then the entire series is equal to zero. Is that correct? and if it is how would I write it up as an answer for my question?