Geoffry B.

# Find the limit (if it exists). lim x→0− x+8/cot x

I am confused as to how to find the limit for this questions as x approaches ) from the left. The cot portion is throwing me off a bit. Any help would be great! Cheers :)math

## 2 Answers By Expert Tutors

By:

Geoffry B.

Hi Tom, Thank you for the explanation. Could you explain why cot goes to inifnite and also 8/infinite=0?
Report

06/24/19

Tom N.

tutor
The cot x is cosx/sinx when x goes to 0 cosx goes to 1 and sinx goes to 0. So 1/0 is defined as infinity. Inifinity is a very large number and so dividing 8 by a very large number gives essentially 0 for a quotient. Another way to do the problem is to rewrite it as lim as x goes to 0 (x+8)sinx/cosx. When you take the limit you get 8*0/1 which gives 0. Hope this helps.
Report

06/24/19

Geoffry B.

That is a wonderful explanation! Cheers!
Report

06/24/19

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.
Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.