JEE Main & Advanced Mathematics Differentiation Question Bank Self Evaluation Test - Limits and Derivatives

  • question_answer
    Let \[f(x)={{x}^{2}}-1,0<x<2\] and \[2x+3,2\le x<3.\] The quadratic equation whose roots are, \[\underset{x\to 2-0}{\mathop{\lim }}\,f(x)\] And \[\underset{x\to 2+\,0}{\mathop{\lim }}\,f(x)\] is

    A) \[{{x}^{2}}-6x+9=0\]

    B) \[{{x}^{2}}-10x+21=0\]

    C) \[{{x}^{2}}-14x+49=0\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[\underset{x\to 2-0}{\mathop{\lim }}\,f(x)=\underset{x\to 2-0}{\mathop{\lim }}\,({{x}^{2}}-1)={{2}^{2}}-1=3\] \[\underset{x\to 2+0}{\mathop{\lim }}\,f(x)=\underset{x\to 2+0}{\mathop{\lim }}\,(2x+3)=2\times 2+3=7\] \[\therefore \] Required quadratic equation is \[{{x}^{2}}-10x+21=0\]


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