CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    x+1, & x\le 1  \\    3-a{{x}^{2}}, & x>1  \\ \end{matrix} \right.\]is continuous at\[x=1,\]then the value of a is:

    A)  \[-1\]                   

    B)         2

    C)  \[-3\]                   

    D)         \[-2\]

    E)  1

    Correct Answer: E

    Solution :

    \[\because \]\[f(x)\]is continuous at\[x=1,\] \[\therefore \]  \[\underset{h\to {{0}^{+}}}{\mathop{\lim }}\,f(1+h)=f(1)\] \[\Rightarrow \]               \[\underset{h\to 0}{\mathop{\lim }}\,3-a{{(1+h)}^{2}}=2\] \[\Rightarrow \]               \[3-a{{(1+0)}^{2}}=2\] \[\Rightarrow \]               \[a=1\]


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