A) 9
B) 4
C) 36
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\] \[=\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}.\frac{\sqrt{x}+3}{\sqrt{x}+3}.\frac{\sqrt{f(x)}+3}{\sqrt{f(x)}+3}\] \[=\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{x-9}.\frac{\sqrt{x}+3}{\sqrt{f(x)}+3}\] \[=\underset{x\to 9}{\mathop{\lim }}\,f(x)\frac{\sqrt{x}+3}{\sqrt{f(x)}+3}\] \[=f(9)\frac{\sqrt{9}+3}{\sqrt{f(9)}+3}\] \[=4.\frac{6}{6}=4\]
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