# Indeterminate Products Giving Me Two Different Limits

1. Dec 9, 2008

### moe darklight

1. The problem statement, all variables and given/known data

lim x-->0 of $$x lnx$$

2. Relevant equations

3. The attempt at a solution

1) $$\frac{lnx}{1/x}$$ = $$\frac{1/x}{-1/x^{2}}$$ = (-x) = 0

2) $$\frac{x}{1/lnx}$$ = $$\frac{1}{1/1/x}$$ = $$\frac{1}{x}$$ = $$\infty$$

Last edited: Dec 9, 2008
2. Dec 9, 2008

### gabbagabbahey

hmmm...are you sure $$\frac{d}{dx} \frac{1}{\ln (x)}=\frac{1}{\frac{1}{x}}$$?

3. Dec 9, 2008

### moe darklight

yea I realized it after a minute of looking at it again. this is exactly the sort of stupid mistake that lowers my marks in tests.

and oops. I didn't see you answer or I wouldn't have edited the entry back.

edit edit: there, I put it back up... but for some reason I think I made a double of the thread... agh. it's 4 AM. I'm tired :rofl:

edit edit edit: and, of course: thanks.

(I go sleep now)

Last edited: Dec 9, 2008