JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer     The value of the\[\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}\]is equal to

    A)  0                                            

    B)  1

    C)  \[e\]                                    

    D)  \[{{e}^{-1}}\]

    Correct Answer: B

    Solution :

                    Let \[A=\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}\] Taking log on both sides, we get \[\log A=\underset{x\to \infty }{\mathop{\lim }}\,\frac{1}{x}\log x\]       \[\Rightarrow \]               \[\log A=0\]                                 \[\left( \because \underset{x\to \infty }{\mathop{\lim }}\,\frac{\log x}{{{x}^{m}}}=0\,\,\forall m>0 \right)\] \[\Rightarrow \]               \[A={{e}^{0}}=1\] \[\Rightarrow \]               \[\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}=1\]

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