lim$$x$1+$

x $+6$x $+2$

The limit$,$ if it exists, is the value L such that

f$($x$)=$

x $+6$x $+2$

can be made as close to L as we choose, by making x sufficiently close to$,$ but to the right of $($or greater than$),$ the value $1.$

We also know by this theorem that if the two$-$sided limit exists, then it is equal to the right$-$hand limit$.$

lim$$x$$a$$f$($x$)=$ L

if and only if

lim$$x$$a$+$f$($x$)=$ L

and

lim$$x$$a$$f$($x$)=$ L

Therefore, when evaluating a one$-$sided limit$,$ it can be useful to check if the standard methods of finding the two$-$sided limit produce a result.

Use the Properties of Limits to rewrite the limit as a combination of limits$.$