These are true provided all the limits involved exist
Laws
1
\lim_{x \to c} (f(x) \pm g(x)) = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)$$
## 2
$$\lim_{x \to c} kf(x) = k \lim_{x \to c} f(x)$$
## 3
$$\lim_{x \to c} (f(x)g(x)) = \left(\lim_{x \to c}f(x)\right)\left(\lim_{x \to c}g(x)\right)$$
## 4
$$\lim_{x \to c}\frac{f(x)}{g(x)} = \frac{\lim\limits_{x \to c} f(x)}{\lim\limits_{x \to c} g(x)}$$
Provided that $\lim\limits_{x \to c}g(x) \neq 0$. If this is an issue, [[Replacement Rule]] can be used
## 5
If $g(x)$ is continuous at $x = b$, and $\lim\limits_{x \to c} f(x) = b$, then
$$\lim_{x \to c}g(f(x)) = g\left(\lim_{x \to c} f(x)\right)$$
# 7
$\lim_{x \to c} f(x)$ only exists if:
$$\lim_{x \to c^-} f(x) = \lim_{x \to c^+} f(x)$$