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If f(x )=sqrt(25-x^(2)), then what is li...

If `f(x )=sqrt(25-x^(2))`, then what is `lim_(x to 1) (f(x)-f(1))/(x-1)` equal to

A

`-(1)/(sqrt24)`

B

`(1)/(sqrt24)`

C

`-(1)/(4sqrt3)`

D

`(1)/(4sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto1)lim(f(x)-f(1))/(x-1)=f'(x)`
Now, `f'(x)=(-2x)/(2sqrt(25-x^(2)))=(-x)/(sqrt(25-x^(2)))`
`f'(1)=(-1)/(sqrt(25-1))=(-1)/(sqrt(24))`
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