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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-2

  • question_answer
    \[\underset{x\to e}{\mathop{\lim }}\,\frac{\log x-1}{x-e}\]is equal to

    A) 0                     

    B) 1               

    C) \[\frac{1}{e}\]                           

    D) \[\frac{1}{2}\]

    Correct Answer: C

    Solution :

    [c] \[\underset{x\to e}{\mathop{\lim }}\,\frac{\log x-1}{x-e}\]which is in \[\frac{0}{0}\]form \[=\underset{x\to e}{\mathop{\lim }}\,\frac{\frac{1}{x}-0}{1-0}\] [By L. Hospital rule] Applying limit \[=\frac{1}{e}\]Hence the option is (c).


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