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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    If\[f\]be a function such that\[f(9)=9\]and \[f(9)=3,\]then \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\]is equal to:

    A)  9                            

    B)         3

    C)  1                            

    D)         6

    E)  \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

    \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)-3}}{\sqrt{x}-3}=\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{\sqrt{f(x)+3}}.\frac{\sqrt{x}+3}{x-9}\] \[=\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{x-9}\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{x}+3}{\sqrt{f(x)}+3}\] \[=f(9)\frac{\sqrt{9}+3}{\sqrt{f(9)}+3}\] \[=3\times \left( \frac{3+3}{\sqrt{9}+3} \right)=3z\]


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