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!

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- Dec 10th 2012, 12:40 PMSteelers72Limits
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 PMPlatoRe: Limits
- Dec 10th 2012, 01:18 PMSteelers72Re: 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 PMPlatoRe: Limits
- Dec 10th 2012, 05:41 PMtopsquarkRe: Limits
Your question has been answered by Plato but I want to draw your attention to the last two lines of your calculation.

You cannot take $\displaystyle \pi$ out of a logarithm. In short:

$\displaystyle ln \left ( \frac{-1}{\pi} \right )$ does not imply $\displaystyle ln(-1) = \pi$.

( ln(-1/pi) doesn't exist anyway, but it's the operation I'm objecting to.)

-Dan