In my book it is mentioned that the proof of this limits result is beyond the scope of the book. But I would love to pursue it's proof anyhow Here's the reasult, $$\lim_{x\to0}[f(x)+g(x)]=\lim_{x\to0}[f(x)]+\lim_{x\to0}[g(x)]$$ The domain and range of $g(x)$ and $f(x)$ are $\Re$ I know this i...