# Evaluate the limit

• Nov 15th 2009, 02:00 PM
Johnny Walker Black
Evaluate the limit
http://i754.photobucket.com/albums/x...Picture1-1.png

In The first problem there was suppose to be a arrow instead of a @ sign.

Not sure where to start, need some help on all three, i'll update as soon as i can get started. Thx
• Nov 15th 2009, 02:03 PM
Jhevon
Quote:

Originally Posted by Johnny Walker Black
http://i754.photobucket.com/albums/x...Picture1-1.png

In The first problem there was suppose to be a arrow instead of a @ sign.

Not sure where to start, need some help on all three, i'll update as soon as i can get started. Thx

For the first, use the fact that $\displaystyle \ln A - \ln B = \ln \frac AB$

For the second, write the function as $\displaystyle \frac x{e^x}$ and apply L'Hopital's rule

For the third, note that you have $\displaystyle \lim_{x \to \infty} x^{1/x} = \lim_{x \to \infty} e^{\ln x^{1/x}} = \lim_{x \to \infty} e^{(\ln x) /x}$ Now find the limit of the power. Again, L'Hopital's rule comes in handy