I'm working with this limit, where I can't use any Maclaurin series, nor can I use L'Hopitals Rule. I'd be pleased if anyone could help me out with this one:
$$\lim_{x\rightarrow 0}\frac{e^{x^{2}}-\cos(x)}{\sin^2x}$$
I'm trying to convert the problem into a limit where I can work with the standard limits, such as $cos(x)/x$, but I'm not successful in doing so.
Thanks for any potential tips!
Best Answer
$$ \frac{\mathrm e^{x^2}-\cos(x)}{\sin^2(x)}=\frac{\mathrm e^{x^2}-1}{x^2}\cdot\frac{x^2}{\sin^2(x)}+\frac{1-\cos(x)}{x^2}\cdot\frac{x^2}{\sin^2(x)} $$