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 $g(x)=\sin(x)$:

Proofs: 1


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983