# Math Help - L'Hopital's Rule

1. ## L'Hopital's Rule

I am to use L'Hopital's Rule on the following problem:

limit as x --> infinity of (1 + (1/x))^x

f(x) = (1 + (1/x))^x
ln[f(x)] = ln [(1 + (1/x))^x] = x ln (1 + (1/x)) = x ln ((x+1)/x)

I can't seem to convert it into a form where I have simply infinity over infinity or zero over zero, because of the 'x' in front of the ln.

:S

2. Originally Posted by niyati
I am to use L'Hopital's Rule on the following problem:

limit as x --> infinity of (1 + (1/x))^x

f(x) = (1 + (1/x))^x
ln[f(x)] = ln [(1 + (1/x))^x] = x ln (1 + (1/x)) = x ln ((x+1)/x)

I can't seem to convert it into a form where I have simply infinity over infinity or zero over zero, because of the 'x' in front of the ln.

:S
Hi,

maybe this will do:

$f(x) = \left(1+\left(\frac1x\right)\right)^x = \left(\frac{x+1}{x}\right)^x = \frac{(x+1)^x}{x^x}$