Properties of limits

Following are some important properties that help to calculate limits:

• $\lim _{x\to a}{\Big [}f(x)\pm g(x){\Big ]}=\lim _{x\to a}f(x)\pm \lim _{x\to a}g(x)$

• $\lim _{x\to a}{\Big [}c\cdot f(x){\Big ]}=c\cdot \lim _{x\to a}f(x)$

• $\lim _{x\to a}{\Big [}f(x)\cdot g(x){\Big ]}=\lim _{x\to a}f(x)\cdot \lim _{x\to a}g(x)$

• $\lim _{x\to a}{\frac {f(x)}{g(x)}}={\frac {\lim \limits _{x\to a}f(x)}{\lim \limits _{x\to a}g(x)}}:\quad {\text{ if }}\lim _{x\to a}g(x)\neq 0$