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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    Let \[f(x)=\left\{ \begin{align}   & {{x}^{2}}+k,\ \ \ \ \text{when}\ \ x\ge 0 \\  & -{{x}^{2}}-k,\ \ \text{when }x<0 \\ \end{align} \right.\]. If the function\[f(x)\] be continuous at \[x=0\], then k =

    A)            0

    B)            1

    C)            2

    D)            ?2

    Correct Answer: A

    Solution :

               Here \[\underset{x\to 0+}{\mathop{\lim }}\,\,\,f(x)=k,\,\,\,\underset{x\to 0-}{\mathop{\lim }}\,f(x)=-k\] and \[f(0)=k\]            But \[f(x)\] is continuous at \[x=0,\] therefore k must be zero.


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