Limiting value

1. Feb 6, 2010

student111

I cant get the following limit to work:

lim(X->0) 1/(ix)*(exp(imx) - 1 ) = m

I'm sorry for the poor notation. I tried expanding the exponential, and L'hopitals rule and combinations of these approaches, but i cant get it to work out. Any help is much appreciated!

2. Feb 6, 2010

HallsofIvy

Staff Emeritus
I assume you mean $\lim_{x\fo 0}\frac{e^{imx}- 1}{ix}$. I can see no reason why L'Hopital's rule would not work:

Both $e^{imx}-1$ and ix go to 0 as x goes to 0.

$\left(e^{imx}\right)'= im e^{imx}$ while (ix)'= i. By L'Hopitals rule, the limit is the same as $\lim_{x\to 0}\frac{im e^{imx}}{i}= m\left(\lim_{x\to 0}e^{imx}\right)= m$.

3. Feb 6, 2010

student111

doh!! I differentiated the whole part instead of nominator and denominator separately..

Thx alot