Geoffry B.

asked • 06/24/19

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

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Tom N. answered • 06/24/19

Strong proficiency in elementary and advanced mathematics

Geoffry B.

Hi Tom, Thank you for the explanation. Could you explain why cot goes to inifnite and also 8/infinite=0?
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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.
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06/24/19

Geoffry B.

That is a wonderful explanation! Cheers!
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06/24/19

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