AP EAMCET · Maths · Limits
If \(f(9)=9\) and \(f^{\prime}(9)=4\), then \(\lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}=\)
- A \(2\)
- B \(3\)
- C \(9\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3} = \lim _{x \rightarrow 9} \frac{\frac{d}{dx}(\sqrt{f(x)}-3)}{\frac{d}{dx}(\sqrt{x}-3)}\) \(= \lim _{x \rightarrow 9} \frac{\frac{f'(x)}{2\sqrt{f(x)}}}{\frac{1}{2\sqrt{x}}}\) \(= \frac{\sqrt{9} f'(9)}{\sqrt{f(9)}}\)…
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