Can someone explain this notation of a limit?

Question

What is the explanation/motivation for this notation? tiontion $$\lim_{x\rightarrow a+0}f(x)$$ I understand it should be equivalent to this notation, which seems much more logical (and simpler): $$\lim_{x\searrow a}f(x)$$

Answer 1

I always saw this form $$\lim_{x\to a^+}$$

I think the reason behind yours is that it means $x=a+\varepsilon \to a + 0$, i.e. $\varepsilon \to 0$ (meaning you're approaching the point from the positive side)