Find a case of the function $\displaystyle f$ and $\displaystyle g$ where $\displaystyle f$ and $\displaystyle g$ do not have limits at a point c, but $\displaystyle f+g$ and $\displaystyle fg$ have limits at c.

Would

$\displaystyle f(x)=(-1)^x$

-and-

$\displaystyle g(x)=(-1)^{x+1}$

work? if $\displaystyle x>1$