Limit Laws

$\displaystyle \boxed{\lim_{x\to c}(f(x)+g(x))=\lim_{x\to c}f(x)+\lim_{x\to c}g(x)}$
provided both $\lim_{x\to c}f(x)$ and $\lim_{x\to c}g(x)$ exist.

Subtraction Law

$\displaystyle \boxed{\lim_{x\to c}(f(x)-g(x))=\lim_{x\to c}f(x)-\lim_{x\to c}g(x)}$
provided both $\lim_{x\to c}f(x)$ and $\lim_{x\to c}g(x)$ exist.

Multiplication Law

$\displaystyle \boxed{\lim_{x\to c}(f(x)\cdot g(x))=\lim_{x\to c}f(x)\cdot\lim_{x\to c}g(x)}$
provided both $\lim_{x\to c}f(x)$ and $\lim_{x\to c}g(x)$ exist.

Division Law

$\displaystyle \boxed{\lim_{x\to c}\frac{f(x)}{g(x)}=\frac{\lim_{x\to c}f(x)}{\lim_{x\to c}g(x)}}$
provided both limits on the right exist, and $\lim_{x\to c}g(x)\neq 0$.

Logarithm Technique

If $\displaystyle \lim_{x\to c}\ln f(x)=a,$ then $\displaystyle \lim_{x\to c}f(x)=e^a.$