◀ ▲ ▶Branches / Analysis / Section: Examples of Limit Calculations
Section: Examples of Limit Calculations
In this section, we will actually calculate some limits for specific functions $f(x)$ as $x$ tends either to a specific real number $a\in\mathbb R$ or to infinity $\infty$. The examples listed below are important since they occur very often as lemmata for other mathematical theorems.
Table of Contents
 Proposition: Limit of 1/n
 Proposition: Limit of the Constant Function
 Proposition: Limit of the Identity Function
 Proposition: Limit of Nth Powers
 Proposition: Convergence Behavior of the Sequence \((b^n)\)
 Proposition: Limit of a Polynomial
 Proposition: Limit of a Rational Function
 Proposition: Limit of Nth Root of a Positive Constant
 Proposition: Limit of Nth Root of N
 Proposition: Limits of General Powers
 Proposition: Square Roots
 Proposition: Limit of Exponential Growth as Compared to Polynomial Growth
 Proposition: Limits of Logarithm in $[0,+\infty]$
 Proposition: Limit of Logarithmic Growth as Compared to Positive Power Growth
 Proposition: Infinitesimal Exponential Growth is the Growth of the Identity Function
 Proposition: Infinitesimal Growth of Sine is the Growth of the Identity Function
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983
 Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition