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JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{|x|}{x}=\]   [Roorkee 1982; UPSEAT 2001]

    A)                 1

    B)                 ?1

    C)                 0

    D)                 Does not exist

    Correct Answer: D

    Solution :

                    Since \[\underset{x\to 0-}{\mathop{\lim }}\,\,\,\frac{|\,\,x\,\,|}{x}=-1\] and  \[\underset{x\to 0+}{\mathop{\lim }}\,\,\,\frac{|\,\,x\,\,|}{x}=1,\] hence limit does not exist.


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