JEE Main & Advanced Mathematics Differentiation Question Bank Self Evaluation Test - Limits and Derivatives

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,{{\left| x \right|}^{[cosx]}}\] is

    A) 1

    B) Does not exist

    C) 0

    D) None of these

    Correct Answer: A

    Solution :

    [a] \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,=\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,{{(x)}^{0}}=1,\] \[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,{{(-x)}^{0}}=\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,1=1\]


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