The role of asymptotic notation in $e^x=1+π‘₯+Θ(π‘₯^2)$?

I’m reading CLRS and there is the following:

When xβ†’0, the approximation of $ e^x$ by $ 1+x$ is quite good: $ $ e^x=1+π‘₯+Θ(π‘₯^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.