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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{{{x}^{2}}+1}-\sqrt[3]{{{x}^{3}}+1}}{\sqrt{{{x}^{4}}+1}-\sqrt[3]{{{x}^{4}}+1}}\]equals

    A)  1                                            

    B)  0

    C)  \[-1\]                                   

    D)  None of these

    Correct Answer: B

    Solution :

                    \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{{{x}^{2}}+1}-\sqrt[3]{{{x}^{3}}+1}}{\sqrt[4]{{{x}^{4}}+1}-\sqrt[5]{{{x}^{4}}+1}}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+\frac{1}{{{x}^{2}}}}-\sqrt[3]{1+\frac{1}{{{x}^{3}}}}}{\sqrt[4]{1+\frac{1}{{{x}^{4}}}}-\sqrt[5]{\frac{1}{x}+\frac{1}{{{x}^{5}}}}}=\frac{1-1}{1-0}=0\]


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