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Proposition: Infinitesimal Growth of Sine is the Growth of the Identity Function
The sine function has the same growth at $0$ as the growth of the identify function, formally
$$ \lim_{x\to 0,~x\neq 0}\frac{\sin(x)}{x}=1.$$
The following figure visualizes the behavior of both functions at $0$, function $f(x)=x$ is drawn together with the function $g(x)=\sin(x)$:
Table of Contents
Proofs: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
