# Homework Help: Limits question

1. Oct 22, 2012

### alejandro7

Hi, I'm having troubles wiith this problem:

limit when x->∞ (1+2^x)^(1/x)

I don't know how to proceed (I know I have to use l'Hospital's rule). It's a ∞^0 indetermination.

Thanks!

2. Oct 23, 2012

### stephenkeiths

Try letting

$y=ln((1+2^{x})^{\frac{1}{x}})$

Then what can you do??

Last edited: Oct 23, 2012
3. Oct 23, 2012

### alejandro7

1/x goes down.

4. Oct 23, 2012

### stephenkeiths

now what form is it in? Can you use L'Hopitals rule now?

5. Oct 23, 2012

### stephenkeiths

Don't forget, that now

$e^{y}=(1+2^{x})^{\frac{1}{x}}$

So when you find y, the limit of

$y=ln((1+2^{x})^{\frac{1}{x}})$

you have to take $e^{y}$ to get the answer to the limit you're looking for.

6. Oct 23, 2012

### alejandro7

Ok I have:

e^lim when x-> of ((ln(1-2^x)/x))

L'Hôpital now?

Last edited: Oct 23, 2012
7. Oct 23, 2012

### stephenkeiths

Well you should have

lim x-->∞ $\frac{ln(1+2^{x})}{x}$

Then use L'Hopitals rule.

You will find the limit of this. To get the answer you want you have to exponentiate it (since you took the natural log in order to find it).