# Limits

• Dec 10th 2012, 12:40 PM
Steelers72
Limits
Evaluate this limit:

lim as x goes to pi from the left ln(cosx/x)

I got the answer as pi

is this right?

My steps:

ln(cospi/pi)

ln(-1/pi)

ln(-1)=pi

Am I right or in the right direction?

Thanks!
• Dec 10th 2012, 12:50 PM
Plato
Re: Limits
Quote:

Originally Posted by Steelers72
Evaluate this limit:
lim as x goes to pi from the left ln(cosx/x)

The logarithm of negative numbers are not defined.
So can the limit exist?
• Dec 10th 2012, 01:18 PM
Steelers72
Re: Limits
so it would be DNE?

I double checked on my calculator and it says ln(-1) would be pi..

Is there an instance, or another way of asking the problem that would make pi the answer? Im just trying to find other ways the teacher could ask this for an exam.

Thanks
• Dec 10th 2012, 01:31 PM
Plato
Re: Limits
Quote:

Originally Posted by Steelers72
I double checked on my calculator and it says ln(-1) would be pi..

Is there an instance, or another way of asking the problem that would make pi the answer? Im just trying to find other ways the teacher could ask this for an exam.

Are you in a complex analysis course?

If so, then $\displaystyle \log(-1)=\pi i$.

But for courses is real analysis, that is not defined.
• Dec 10th 2012, 05:41 PM
topsquark
Re: Limits
Quote:

Originally Posted by Steelers72
ln(-1/pi)

ln(-1)=pi

You cannot take $\displaystyle \pi$ out of a logarithm. In short:
$\displaystyle ln \left ( \frac{-1}{\pi} \right )$ does not imply $\displaystyle ln(-1) = \pi$.