Ononot — Let f(x) be defined as f(x) = \sum{n=1}^{\infty} \frac{x^n}{

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Limits & Continuityhard

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Let $f(x)$ be defined as $f(x) = \sum_{n=1}^{\infty} \frac{x^n}{n!}$ . Which of the following statements regarding the limit $\lim_{x \to \infty} \frac{f(x)}{x^k}$ is true for any fixed $k \in \mathbb{N}$ ?