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

  • question_answer
    Let \[f(x)=x{{(-1)}^{[1/x]}},x\ne 0,\] where [x] denotes the greatest integer less than or equal to x then, \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\]

    A) Does not exist

    B) 2

    C) 0

    D) -1

    Correct Answer: C

    Solution :

    [c] \[\because [1/x]=integer\] \[\therefore {{(-1)}^{[1/x]}}=1or-1\] \[\underset{x\to 0}{\mathop{\lim }}\,x{{(-1)}^{[1/x]}}=\underset{h\to 0}{\mathop{\lim }}\,(h)(1or-1)=0\] \[=\underset{h\to 0}{\mathop{\lim }}\,(-h)\,(1or-1)=0\]     


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