Exponential Function Limit

[Fabufabu]

I'm trying to simplify the following limit to either evaluate it or find that it doesn't exist.

lim (e^(3x)-e^x)/(e^x-1)
x->o


I've done some algebraic manipulation to try and get (e^x-1)/x isolated but so far I've just been going in circles.

Any clues?

 

[BigGlenntheHeavy]

\(\displaystyle \lim_{x\to0}\frac{e^{3x}-e^{x}}{e^{3}-1} \ = \ \lim_{x\to0}\frac{0}{e^{3}-1} \ = \ 0\)

 

[Fabufabu]

Whoops, fixed a typo in the original post, denominator is actually e^x-1, not e^3-1.

 

[daon]

Let y = e^x. Then you have lim y->1 [y^3-y]/[y-1]. Then factor the top and cancel the discontinuity.

 

[Fabufabu]

Thanks for the help, substituting a variable for e^x made that problem a walk in the park, wish I'd thought of that earlier. Thanks again, to both of you.