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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2006

  • 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)  \[2\,\log 5\]

    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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