# Is this true?

• April 22nd 2010, 05:47 PM
HD09
Is this true?
$\lim_{x\rightarrow\infty}f(x) = e^{\lim_{x\rightarrow\infty}ln(f(x))}$

I think I've seen or used this before but it might've just been something similar, I don't have my calculus book handy.
• April 22nd 2010, 05:52 PM
Drexel28
Quote:

Originally Posted by HD09
$\lim_{x\rightarrow\infty}f(x) = e^{\lim_{x\rightarrow\infty}ln(f(x))}$

I think I've seen or used this before but it might've just been something similar, I don't have my calculus book handy.

If the limit exists, yes. The quick way using only continuity is that $\lim_{x\to\infty}f(x)=\lim_{z\to 0}f\left(\frac{1}{z}\right)=\lim_{z\to 0}\text{exp}\left(\ln\left(f\left(\frac{1}{z}\righ t)\right)\right)=\text{exp}\left(\lim_{z\to 0}\ln\left(f\left(\frac{1}{z}\right)\right)\right)$ and work backwards.