Limit Laws

Limit Laws

If:

$$\lim_{x\to a}f(x)=L_1$$

and:

$$\lim_{x\to a}g(x)=L_2$$

then:

$$\lim_{x\to a}[f(x)+g(x)]=L_1+L_2$$

$$\lim_{x\to a}[f(x)-g(x)]=L_1-L_2$$

$$\lim_{x\to a}[f(x)g(x)]=L_1L_2$$

$$\lim_{x\to a}\frac{f(x)}{g(x)}=\frac{L_1}{L_2},\quad L_2\neq0$$

Usage

- Used to evaluate limits by separating complicated expressions into simpler functions.