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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & \,\,\,\,{{x}^{2}},\,\text{when}\,x\le 1 \\  & x+5,\text{when }x>\text{1} \\ \end{align} \right.\], then [AISSE 1983]

    A)            \[f(x)\]is continuous at \[x=1\]

    B)            \[f(x)\]is discontinuous at\[x=1\]

    C)            \[\underset{x\to 1}{\mathop{\lim }}\,f(x)=1\]                           

    D)            None of these

    Correct Answer: B

    Solution :

               \[\underset{x\to 1-}{\mathop{\lim }}\,f(x)=1,\underset{x\to 1+}{\mathop{\lim }}\,f(x)=6.\]


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