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If f(9)=9andf'(9)=4 then what is lim(xto...

If `f(9)=9andf'(9)=4` then what is `lim_(xto9) (sqrtf(x)-3)/(sqrtx-4)` equal to?

A

36

B

9

C

4

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto0)lim(sqrt(f(x)-3))/(sqrt(x-3))=underset(xto0)lim((1)/(2sqrtf(x))f'(x))/(1/(2sqrtx).1)`
(By L' Hospital rule)
`underset(xto0)lim(f'(x)xxsqrtx)/(sqrtf(x))=(f'(9)xxsqrt9)/(sqrtf(9))`
`=(4xx3)/(sqrt9)=(4xx3)/(3)=4`
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