limit laws

Sum Rule

${\lim }_{x\to c}\left[f(x)+g(x)\right]={\lim }_{x\to c}f(x)+{\lim }_{x\to c}g(x)$

Difference Rule

${\lim }_{x\to c}\left[f(x)-g(x)\right]={\lim }_{x\to c}f(x)-{\lim }_{x\to c}g(x)$

Product Rule

${\lim }_{x\to c}\left[f(x)\cdot g(x)\right]={\lim }_{x\to c}f(x)\cdot {\lim }_{x\to c}g(x)$

Constant Multiple Rule

${\lim }_{x\to c}k\cdot f(x)=k{\lim }_{x\to c}f(x)$

Quotient Rule

${\lim }_{x\to c}\frac{f(x)}{g(x)}=\frac{{\lim }_{x\to c}f(x)}{{\lim }_{x\to c}g(x)}$

Power Rule

${\lim }_{x\to c}f(x{)}^r={\left({\lim }_{x\to c}f(x)\right)}^r$