BCECE Engineering BCECE Engineering Solved Paper-2010

  • question_answer If \[f(9)=9,\]\[f(9)=4,\]then \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\] equals

    A)  9                            

    B)         4            

    C)  36                         

    D)         None of these

    Correct Answer: B

    Solution :

                    \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\] \[=\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}.\frac{\sqrt{x}+3}{\sqrt{x}+3}.\frac{\sqrt{f(x)}+3}{\sqrt{f(x)}+3}\] \[=\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{x-9}.\frac{\sqrt{x}+3}{\sqrt{f(x)}+3}\]                 \[=\underset{x\to 9}{\mathop{\lim }}\,f(x)\frac{\sqrt{x}+3}{\sqrt{f(x)}+3}\] \[=f(9)\frac{\sqrt{9}+3}{\sqrt{f(9)}+3}\] \[=4.\frac{6}{6}=4\]

adversite


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