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Meaning of $ e^x = 1 + x + Θ(x^2)$?
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Problem
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?
$$e^x = 1 + x + Θ(x^2).$$
How is it to be interpreted, what is the role of asymptotic notation here?
Solution
There are constants $c,C,\epsilon > 0$, such that $1+x+cx^2 \le e^x \le 1+x+Cx^2$ whenever $|x| \leq \epsilon$.
Context
StackExchange Computer Science Q#103593, answer score: 4
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