Does limit means replacing $x$ for a number? I don't understand limit so much. For example I see $\lim_{x \to -3}$. And I always just put $-3$ everywhere I see $x$. I feel like I'm doing something wrong, but it seems correct all the time.

One of the most important limits is the definition of the derivative
$$
\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}
$$
and you cannot substitute $h=0$ in that fraction.
