A) \[n=0\]only
B) n is any whole number
C) \[n=2\]only
D) no value of n
Correct Answer: B
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{e}^{x}}}\] \[\left( form\frac{\infty }{\infty } \right)\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{n{{x}^{n-1}}}{{{e}^{x}}}=....=\underset{x\to \infty }{\mathop{\lim }}\,\frac{n!}{{{e}^{x}}}=0\] where n is any whole number as\[n!\]is defined for the integers and 0.
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