I have worked out the following but need to prove it.

lim

x-->0

x^2

1-e^x^2

= -1

Can anyone help?

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- Jul 19th 2011, 02:00 AMArronLimits
I have worked out the following but need to prove it.

lim

x-->0

__x^2__

1-e^x^2

= -1

Can anyone help? - Jul 19th 2011, 02:03 AMProve ItRe: Limits
It's of the indeterminate form $\displaystyle \displaystyle \frac{0}{0}$ so you can use L'Hospital's Rule.

- Jul 19th 2011, 02:15 AMCaptainBlackRe: Limits
- Jul 19th 2011, 04:22 AMJesterRe: Limits
If you let $\displaystyle t = x^2$, you could write your limit as

$\displaystyle \displaystyle - \dfrac{1}{\lim_{t \to 0} \dfrac{e^t-1}{t}}$

with the limit now something you might recognize.