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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)\,=\,\left\{ \begin{matrix}    \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x} & \text{,for}-1\le x<0  \\    2{{x}^{2}}+3x-2 & \text{,}\,\text{for }\,0\le \,x\le 1  \\ \end{matrix} \right.\], is continuous at \[x=0\],  then \[k=\] [EAMCET 2003]

    A)            ? 4

    B)            ? 3

    C)            ? 2

    D)            ? 1

    Correct Answer: C

    Solution :

               L.H.L. \[=\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}=k\]            R.H.L. \[=\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,(2{{x}^{2}}+3x-2)=-2\]            Since it is continuous, L.H.L = R.H.L Þ \[k=-2\].


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