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JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{\frac{1}{x}}}}{{{e}^{\left( \frac{1}{x}+1 \right)}}}=\] [DCE 1999]

    A)                 0

    B)                 1

    C)                 Does not exist

    D)                 None of these

    Correct Answer: D

    Solution :

                    \[\underset{x\to 0}{\mathop{\text{lim}}}\,\frac{{{e}^{1/x}}}{{{e}^{\left( \frac{1}{x}+1 \right)}}}=\underset{x\to 0}{\mathop{\text{lim}}}\,\frac{{{e}^{1/x}}}{{{e}^{\frac{1}{x}}}.e}\]\[=\underset{x\to 0}{\mathop{\text{lim}}}\,\frac{1}{e}={{e}^{-1}}\].


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