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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2008

  • question_answer
        The value of\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{5}^{x}}-{{5}^{-x}}}{2x}\]is

    A)  log 5                                     

    B)  0

    C)  1                                            

    D)  \[2\text{ }log\text{ }5\]

    Correct Answer: A

    Solution :

                    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{5}^{x}}-{{5}^{-x}}}{2x}\] Applying L- Hospitals rule \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{5}^{x}}\log 5+{{5}^{-x}}\log 5}{2}\] \[=\frac{\log 5+\log 5}{2}=\log 5\]


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