A) 9
B) 3
C) 1
D) 6
E) \[\frac{2}{3}\]
Correct Answer: B
Solution :
\[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)-3}}{\sqrt{x}-3}=\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{\sqrt{f(x)+3}}.\frac{\sqrt{x}+3}{x-9}\] \[=\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{x-9}\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{x}+3}{\sqrt{f(x)}+3}\] \[=f(9)\frac{\sqrt{9}+3}{\sqrt{f(9)}+3}\] \[=3\times \left( \frac{3+3}{\sqrt{9}+3} \right)=3z\]You need to login to perform this action.
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