Breaking my limits

Calculus Level 3

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

Let nn be a certain positive integer satisfying the equation above, which of the following options must be true?

Clarification: ee denotes the Euler's number, e2.71828e \approx 2.71828.


Source: IIT - 1992.
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