Evaluate the limit

**Johnny Walker Black** · November 15th 2009, 03:00 PM

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

**Jhevon** · November 15th 2009, 03:03 PM

Originally Posted by Johnny Walker Black

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 $\ln A - \ln B = \ln \frac AB$

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

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

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