Struggling with a Limit: Help Appreciated!

[student111]

I can't 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'hospital's rule and combinations of these approaches, but i can't get it to work out. Any help is much appreciated!

 

[HallsofIvy]

I can't 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'hospital's rule and combinations of these approaches, but i can't get it to work out. Any help is much appreciated!

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.

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

 

[student111]

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

Thx a lot