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BCECE Engineering BCECE Engineering Solved Paper-2004

  • question_answer
    The value of \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+{{x}^{4}}}-(1+{{x}^{2}})}{{{x}^{2}}}\]is equal to

    A)  0                                            

    B)  \[-1\]

    C)  2                            

    D)         none of these

    Correct Answer: A

    Solution :

    \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+{{x}^{4}}}-(1+{{x}^{2}})}{{{x}^{2}}}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+\frac{1}{{{x}^{4}}}-\left( 1+\frac{1}{{{x}^{2}}} \right)}}{1}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+0}-(1+0)}{1}\] \[=0\]


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