Indeterminate Products Giving Me Two Different Limits

[moe darklight]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

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

 

[gabbagabbahey]

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

 

[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

edit edit edit: and, of course: thanks.

(I go sleep now)