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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

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

    A)  3                                            

    B)         0

    C)         \[-6\]                                   

    D)         \[\frac{1}{6}\]

    E)         \[-\frac{1}{6}\]

    Correct Answer: B

    Solution :

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


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