# Meaning of $e^x = 1 + x + Θ(x^2)$?

In the CLRS chapter 3: When $$x → 0$$, the approximation of $$e^x$$ by $$1+x$$ is quite good:

$$e^x = 1 + x + Θ(x^2).$$

How is it to be interpreted, what is the role of asymptotic notation here?

There are constants $$c,C,\epsilon > 0$$, such that $$1+x+cx^2 \le e^x \le 1+x+Cx^2$$ whenever $$|x| \leq \epsilon$$.
This is an example of "placeholder notation". In such expressions, you should mentally replace "$$\Theta(x^2)$$" with "$$f$$, for some function $$f=\Theta(x^2)$$".