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.
- Why do they use $ Θ$ here and why do they use $ =$ sign?
- 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 $ ?
- 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.