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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 13

  • question_answer
    Let \[f(x)=\frac{\sin x({{2}^{x}}+{{2}^{-x}})\sqrt{{{\tan }^{-1}}({{x}^{2}}-x+1)}}{{{(7{{x}^{2}}+3x+1)}^{3}}}\]Then  is equal to

    A)  \[0\]                      

    B)         \[\sqrt{\pi }\]          

    C)  \[\pi \]                     

    D)         Does not exist

    Correct Answer: B

    Solution :

      [b]  \[f'(0)=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{f(x)-f(0)}{x-0}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{\frac{\sin x}{x}\left( {{2}^{x}}+{{2}^{-x}} \right)\sqrt{{{\tan }^{-1}}\left( {{x}^{2}}-x+1 \right)}}{{{\left( 7{{x}^{2}}+3x+1 \right)}^{3}}}=\sqrt{\pi }\]       


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