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What is lim(x to 2) (2-x)/(x^(3)-8) equa...

What is `lim_(x to 2) (2-x)/(x^(3)-8)` equal to ?

A

`(1)/(8)`

B

`-(1)/(8)`

C

`(1)/(12)`

D

`-(1)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xto2)lim(2-x)/(x^(3)-8)=underset(xto2)lim(2-x)/((x-2)(x^(2)+2x+4))`
`=underset(xto2)lim(-1)/(x^(2)+2x+4)`
Putting x=2, we get
`(-1)/(2^(2)+4+4)=-(1)/(12)`
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