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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\,{{(1-ax)}^{1/x}}\] is equal to :

    A)  \[{{e}^{-a}}\]                                   

    B)  e

    C)  \[{{e}^{a}}\]                                     

    D)  1

    Correct Answer: A

    Solution :

    We have \[=\underset{x\to 0}{\mathop{\lim }}\,\,{{(1-ax)}^{1/x}}\]                 \[\underset{x\to 0}{\mathop{\lim }}\,\,{{(1-ax)}^{-\frac{1}{ax{{]}^{-a}}}}}\]                 \[={{e}^{-a}}\]                   \[\left[ \underset{x\to 0}{\mathop{\lim }}\,\,\,{{(1-ax)}^{\frac{1}{-ax}}}=e \right]\]


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