TS EAMCET · Maths · Limits
If \(\mathrm{f}(9)=9\) and \(\mathrm{f}^{\prime}(9)=4\), then \(\lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}=\)
- A \(3\)
- B \(4\)
- C \(6\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3} \\ = & \lim _{x \rightarrow 9} \frac{\frac{f^{\prime}(x)}{2 \sqrt{f(x)}}}{\frac{1}{2 \sqrt{x}}} \quad\left(\frac{0}{0} \text { form }\right) \\ = & \lim _{x \rightarrow 9}…
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