JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    \frac{2}{5-x}, & \text{when }x<3  \\    5-x, & \text{when }x>3  \\ \end{matrix} \right.\],  then

    A)                 \[\underset{x\to 3+}{\mathop{\lim }}\,f(x)=0\]

    B)                 \[\underset{x\to 3-}{\mathop{\lim }}\,f(x)=0\]

    C)                 \[\underset{x\to 3+}{\mathop{\lim }}\,f(x)\ne \underset{x\to 3-}{\mathop{\lim }}\,f(x)\]

    D)                 None of these

    Correct Answer: C

    Solution :

                    \[\underset{x\to 3+}{\mathop{\lim }}\,f(x)=5-3=2,\,\underset{x\to 3-}{\mathop{\lim }}\,f(x)=\frac{2}{5-3}=1.\]


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