$\lim_{x \to 0}(f+g)$ if $\lim_{x \to 0}g$ does not exist Let $f$ such that $\lim_{x\to 0}f(x)=\infty$ and let $g(x)=\sin(\frac{1}{x})$. I know that $g$ does not have a limit at $x=0$, but what about $\lim_{x\rightarrow 0}(f(x)+g(x))$?
Thanks!

Always limit is infinity considering your problem.
