Thread: 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!

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?

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

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 .

But for courses is real analysis, that is not defined.

Originally Posted by Steelers72

ln(-1/pi)

ln(-1)=pi

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 out of a logarithm. In short:
does not imply .

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

-Dan