Question

If f(9) = 9 and f'(9)= 4 , then $\underset{x\to 9}{lim}\frac{\sqrt{f\left(x\right)}-3}{\sqrt{x}-3}$ is equal to-

• A. 1
• B. 3
• C. 4
• D. 9

Answer 1

The correct option is C 4

the mistake in the question is $f\left(9\right)=9,f^{\prime }\left(9\right)=4$

$\underset{x\to 9}{lim}\frac{\sqrt{f\left(x\right)}-3}{\sqrt{x}-3}=\underset{x\to 9}{lim}\frac{\frac{f^{\prime }\left(x\right)}{2\sqrt{f\left(x\right)}}}{\frac{1}{2\sqrt{x}}}=4$