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If f(9)=9" and f'"(9)=4 then Lt(x to 9)(...

If `f(9)=9" and f'"(9)=4` then `Lt_(x to 9)(sqrt(f(x))-3)/(sqrt(x)-3)` is equal to

A

9

B

4

C

36

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
` underset(xto9)lim(sqrt(f(x))-3)/(sqrt(x)-3)=underset(xto9)lim(f(x)-9)/(x-9)xx(sqrt(x)+3)/(sqrt(f(x))+3)`
`impliesunderset(xto9)lim(sqrt(f(x))-3)/(sqrt(x)-3)`
`=f'(9)xx{(sqrt(9)+3)/(sqrt(f(9)+3))}=f'(9)xx(3+3)/(3+3)=f'(9)=4`
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