$bvv$ Constant multiple law for limits

e $vv$ Quotient law for limits

$g^V$ Sum law for limits

c R Root law for limits

Power law for limits

d $$ Difference law for limits

$fvv$ Product law for limits

a$.\underset{xa}{lim}(f(x){)}^n=(\underset{xa}{lim}f(x){)}^n=L^n$ for every positive integer $n$

b$.\underset{xa}{lim}(f(x)*g(x))=\underset{xa}{lim}f(x)*\underset{xa}{lim}g(x)=L*M$

c$.\underset{xa}{lim}\sqrt[n]{f(x)}=\sqrt[n]{\underset{xa}{lim}f(x)}=\sqrt[n]{L}$ for all $L$ if $n$ is odd and for $L0$ if $n$ is even and $f(x)0$

d$.\underset{xa}{lim}(f(x)-g(x))=\underset{xa}{lim}f(x)-\underset{xa}{lim}g(x)=L-M$

e$.\underset{xa}{lim}\frac{f(x)}{g(x)}=\frac{\underset{xa}{lim}f(x)}{\underset{xa}{lim}g(x)}=\frac{L}{M}$ for $M0$

f$.\underset{xa}{lim}cf(x)=c*\underset{xa}{lim}f(x)=cL$