Properties Of Limits

Let $b$ and $c$ be real numbers, let $n$ be a positive integer, and let $f$ and $g$ be functions with the following limits:

$$\lim_{x \to c}f(x)=L \quad\lim_{x\to c}g(x)=K$$

$$\lim_{x\to c} b=b$$ Constant:

$$\lim_{x\to c} [b f(x)]=bL$$ Scalar multiple:

$$\lim_{x\to c} [f(x)\pm g(x)]=L\pm K$$ Sum or difference:

$$\lim_{x\to c} [f(x)g(x)]=LK$$ Product:

$$\lim_{x\to c} \frac{f(x)}{g(x)}=\frac{L}{K},\quad K\ne 0$$ Quotient:

$$\lim_{x\to c} [f(x)]^n=L^n$$ Power: