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If f(x)=(sqrt(x+3)-2)/(x^(3)-1) for x n...

If `f(x)=(sqrt(x+3)-2)/(x^(3)-1)` for `x ne 1` is continuous at x = 1. then f(1) is

A

12

B

8

C

`(1)/(12)`

D

`(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `f(x)=(sqrt(x+3)-2)/(x^(3)-1)`
Now, `lim_(x to 0) (sqrt(x+3)-2)/(x^(3)-1^(3))xx(sqrt(x+3)+2)/(sqrt(x+3)+2)`
` =lim_(x to 1) (x-1)/((x-1)(x^(2)+x+1)(sqrt(x+3)+2))`
`=(1)/(3(4))=(1)/(12)`
Since f continuous at x = 1,
`therefore lim_(x to1)f(x)=f(1)=(1)/(12)`
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