# Quick limit help.

• Sep 23rd 2008, 08:42 PM
cowboys111
Quick limit help.
Hi, im trying to find the limit of xln(x) as it approaches 0+. I think the limit of ln(x) is undefined making it infinite right? But would the x at the begining make the limit approach 0?
Thank you.
• Sep 23rd 2008, 08:48 PM
Chris L T521
Quote:

Originally Posted by cowboys111
Hi, im trying to find the limit of xln(x) as it approaches 0+. I think the limit of ln(x) is undefined making it infinite right? But would the x at the begining make the limit approach 0?
Thank you.

Note that $\lim_{x\to{0^+}}x\ln x=\lim_{x\to{0^+}}\frac{\ln x}{\frac{1}{x}}$

you have the indeterminate case $\frac{\infty}{\infty}$.

We can now apply L'Hopital's rule:

$\therefore\lim_{x\to{0^+}}\frac{\ln x}{\frac{1}{x}}=\lim_{x\to{0^+}}\frac{\frac{1}{x}} {-\frac{1}{x^2}}=\lim_{x\to{0^+}}-\frac{1}{\frac{1}{x}}=\lim_{x\to{0^+}}-x=\color{red}\boxed{0}$

Does this make sense?

--Chris
• Sep 23rd 2008, 10:58 PM
cowboys111
Yes it does, thank you.