## The role of asymptotic notation in $e^x=1+𝑥+Θ(𝑥^2)$?

I’m reading CLRS and there is the following:

When x→0, the approximation of $$e^x$$ by $$1+x$$ is quite good: $$e^x=1+𝑥+Θ(𝑥^2)$$

I suppose I understand what means this equation from math perspective and, also, there is an answer in another cs question. But I don’t understand some things, so have a few questions.

1. Why do they use $$Θ$$ here and why do they use $$=$$ sign?
2. Is it possible to explain how the notation here is related to the author’s conclusion that $$e^x$$ is very close to $$1 + x$$ when $$x \rightarrow 0$$?
3. Also, how is it important here that $$x$$ tends to $$0$$ rather than to $$\infty$$ as we usually use asymptotic notations?

I’m sorry if there are a lot of questions and if they are stupid, I’m just trying to master this topic.