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

  • question_answer
    If \[\underset{x\to \infty }{\mathop{\lim }}\,\left\{ \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax+b) \right\}=2\], then

    A) \[a=1,\text{ }b=1\]      

    B) \[a=1,\text{ }b=2\]

    C) \[a=1,\text{ }v=-2\]     

    D) None of these

    Correct Answer: C

    Solution :

    [c] \[\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax+b) \right)=2\] Or \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{3}}(1-a)-b{{x}^{3}}-ax+(1-b)}{{{x}^{2}}+1}=2\] Or \[1-a=0\] and \[-b=2\] Or \[a=1,\]\[b=-2\]


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