Not sure how to prove the following. Link to Equation
$$e^x=\sum_{i=0}^{m-1}\frac{x^i}{i!}+\Theta(x^m)\,,$$ for all $m=1,2,\cdots$
2026-03-29 11:42:30.1774784550
Aysmptotic Analysis Proof
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If $m=1$ this is $e^x = 1+\Theta(x)$ which is not true for large $x$.
You need a restriction such as $|x| \le 1$.