calculus - Find $limlimits_{ntoinfty}f^{(n)}(x)$ and $limlimits_{ntoinfty}g^{(n)}(x)$

Let's consider $f, g: (0, +\infty) \rightarrow\mathbb{R}$, $f(x)=\displaystyle\frac{\sin x}{x}$, $g(x)=\displaystyle\frac{\cos x}{x}$. Find the following limits

$$\lim_{n\to\infty}f^{(n)}(x)$$

$$\lim_{n\to\infty}g^{(n)}(x)$$

where $f^{(n)}$ and $g^{(n)}$ are the $n$th derivatives of $f(x)$, respectively $g(x)$.
It's a problem I thought of last days and I didn't guess the answer by trying to look at the first derivatives of both functions. What should I do here to get the limits? Thanks.