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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{e}^{x}}}=0\] for                                  [IIT 1992]

    A) No value of n

    B) n is any whole number

    C) \[n=0\] only

    D) \[n=2\] only

    Correct Answer: B

    Solution :

    • \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{e}^{x}}}=\underset{x\to \infty }{\mathop{\lim }}\,n\frac{{{x}^{n-1}}}{{{e}^{x}}}=......\]\[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{n\,\,!}{{{e}^{x}}}=\frac{n\,\,!}{\infty }=0\],                    
    • where n is any whole number \[(\,\because \,\,n\,!\] is defined for all positive integers including zero).


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