# proof writing – Question about limits at infinity.

if for example I have fucntions $$f$$ and $$g$$, we’ve prove in class that if
$$lim _{xto a}left(fleft(xright)-gleft(xright)right)=L$$

$$or$$

$$lim _{xto a}left(fleft(xright)cdot gleft(xright)right)=L$$

then both limits of $$f$$ and $$g$$ exist, or both don’t exist.

$$lim _{xto ∞/-∞}left(fleft(xright)-gleft(xright)right)=L$$
$$or$$
$$lim _{xto ∞/-∞}left(fleft(xright)cdot gleft(xright)right)=L$$