Breaking my limits

Calculus Level 4

\[ \large \lim_{x\to \infty} \frac{nx^n}{e^x} = 0\]

Let \(n\) be a certain positive integer satisfying the equation above, which of the following options must be true?

Clarification: \(e\) denotes the Euler's number, \(e \approx 2.71828\).


Source: IIT - 1992.
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