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## Homework Statement

[tex]\lim_{x\to0}[\frac{1}{x^2} - \frac{\cos(x)}{\sin(x)^2}][/tex]

I'm supposed to use Maclaurin series to evaluate this limit. The instructions suggest, as a hint:

"First combine the fractions. Then find the first term of the denominator series and the first term of the numerator series".

## Homework Equations

- Maclaurin series for sin(x)

- Maclaurin series for cos(x)

- L'Hopital's rule

## The Attempt at a Solution

Graphing it I know the limit is (-1/6), but I can't show it.

I tried separating each function into its respective series, and I've tried taking several derivatives to see if L'Hopital's rule can make the limit apparent, but I'm not having much luck. I've also tried using different trig identities to try to help, but without much luck.

Any suggestions?