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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & a{{x}^{2}}-b,\,\,\text{when }0\le x<1 \\  & \,\,\,\,\,\,\,\,\,\,\,\,2,\text{when }x=1 \\  & \,\,\,\,x+1,\,\,\text{when1}<x\le 2 \\ \end{align} \right.\]is continuous at \[x=1\], then the most suitable value of a, b are       [BIT Ranchi 1983]

    A)            \[a=2,\ b=0\]

    B)            \[a=1,\ b=-1\]

    C)            \[a=4,\ b=2\]

    D)            All the above

    Correct Answer: D

    Solution :

               \[\underset{x\to 1-}{\mathop{\lim }}\,f(x)=a-b,\,\,\underset{x\to 1+}{\mathop{\lim }}\,f(x)=2\,\,\Rightarrow a-b=2\]            All the given sets of a, b make \[f(x)\] continuous at x=1.


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