The limits of the sum of functions whose limits do not exist I have a homework problem that I'm not sure how to start. I tried Google for similar examples it didn't turn up anything. Could someone tell me the name of the concept to look into? The problem is as follows:
Show by example that $\lim_{x\to c}f(x) + g(x)$ can exist even if both $\lim_{x\to c}f(x)$ and $\lim_{x\to c}g(x)$ do not exist.

What about $f(x)=x$ and $g(x)=-x$.  Neither limit as $x\to\infty$ exists as a real number, yet the limit of the sum is $0$.  Or $f(x)=sinx$ and $g(x)=-sinx$.  This time neither limit exists (as a real number OR +/-$\infty$, but the limit of the sum is $0$.
To get this phenomenon as $x$ approaches some real number $c$, think of a function $f$ with a vertical asymptote at $x=c$, and then take that function's negation as $g$.
