# Math Help - Problem rewriting function as a power series

1. ## Problem rewriting function as a power series

Using known power series representations find
limit as x => 0 of (1 - e^(x^4)) / (x^2 * sin (x^2))

I cannot figure out how to rewrite this in any way that involves (1 / (1 - x)) which is how we rewrote most functions as power series in examples.

How can i rewrite this function as a power series?

2. Originally Posted by crymorenoobs
Using known power series representations find
limit as x => 0 of (1 - e^(x^4)) / (x^2 * sin (x^2))

I cannot figure out how to rewrite this in any way that involves (1 / (1 - x)) which is how we rewrote most functions as power series in examples.

How can i rewrite this function as a power series?
You only need to use the first few terms of each series:

$\lim_{x \rightarrow 0} \frac{1 - (1 + x^4 + x^8 + ....)}{x^2 (x^2 - x^6/6 + ....)}$

$= \lim_{x \rightarrow 0} \frac{-x^4 - x^8 - ....}{x^4 (1 - x^4/6 + ....)} = ....$

3. Oh ok thank you.

4. $\frac{1-e^{x^{4}}}{x^{2}\sin x^{2}}=\frac{1-e^{x^{4}}}{x^{4}}\cdot \frac{x^{2}}{\sin x^{2}},$ and the limit is 1.