To analyze the limit of $\cos(x)$ as $x \to 3$ using the $\epsilon$-$\delta$ definition, we need to express how the values of $\cos(x)$ approach $0$. However, $\lim_{x \to 3} \cos(x) \neq 0$ because the cosine function is continuous and periodic, and $\cos(3)$ has a definite value.

Instead, let us explore the general $\epsilon$-$\delta$ framework. Here's how it works:

General $\epsilon$-$\delta$ Framework:

The limit of a function $f(x)$ as $x \to c$ is $L$ if, for every $\epsilon > 0$, there exists a $\delta > 0$ such that: $0 < |x - c| < \delta \implies |f(x) - L| < \epsilon.$

Applying to $\cos(x)$:

For $\cos(x)$, we calculate: $\cos(3) = \text{a specific numerical value}.$

Thus, if the question is whether (\lim_{x \to 3} returns !! user... Reminder of the equation...?we??