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Proposition: Limits of General Powers
The limits of general powers $x^\alpha$ and $x^{-\alpha}$ for a fixed $\alpha > 0$ and for $x\searrow 0$ are given by
$$\lim_{x\searrow 0}x^\alpha=0,$$
$$\lim_{x\searrow 0}\frac 1{x^\alpha}=\infty,$$
$$\lim_{x\searrow 0}x^x=1.$$
Table of Contents
Proofs: 1 Corollaries: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
