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If f be a function such that f(9)=9 and ...

If `f` be a function such that `f(9)=9` and `f'(9)=3`, then `lim_(xto9)(sqrt(f(x))-3)/(sqrt(x)-3)` is equal to

A

9

B

3

C

1

D

None of these

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Verified by Experts

The correct Answer is:
B
`lim_(xto9)(sqrt(c(x))-3)/(sqrt(x)-3)`
`=lim_(xto9)(f(x)-9)/(x-9)xx(sqrt(x)+3)/(sqrt(f(x))+3)`
`f'(9)xx((sqrt(9)+3)/(sqrt(f(9))+3))`
`=f'(9)xx(3+3)/(3+3)=3`
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