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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    \frac{{{x}^{2}}-9}{x-3}\,, & \text{if }x\ne 3  \\    2x+k\,, & \text{otherwise}  \\ \end{matrix} \right.\], is continuous at \[x=3,\] then \[k=\]                  [Kerala (Engg.) 2002]

    A)            3

    B)            0

    C)            ?6

    D)            1/6

    Correct Answer: B

    Solution :

               \[\underset{x\to 3}{\mathop{\lim }}\,f(x)=\underset{x\to 3}{\mathop{\lim }}\,\frac{{{x}^{2}}-9}{x-3}=\underset{x\to 3}{\mathop{\lim }}\,(x+3)=6\]            and \[f(3)=2(3)+k=6+k\]            \[\because f\] is continuous at \[x=3\]; \ \[6+k=6\Rightarrow k=0\].


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