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.

  1. Proposition: Limit of 1/n
  2. Proposition: Limit of the Constant Function
  3. Proposition: Limit of the Identity Function
  4. Proposition: Limit of Nth Powers
  5. Proposition: Convergence Behavior of the Sequence \((b^n)\)
  6. Proposition: Limit of a Polynomial
  7. Proposition: Limit of a Rational Function
  8. Proposition: Limit of Nth Root of a Positive Constant
  9. Proposition: Limit of Nth Root of N
  10. Proposition: Limits of General Powers
  11. Proposition: Square Roots
  12. Proposition: Limit of Exponential Growth as Compared to Polynomial Growth
  13. Proposition: Limits of Logarithm in $[0,+\infty]$
  14. Proposition: Limit of Logarithmic Growth as Compared to Positive Power Growth
  15. Proposition: Infinitesimal Exponential Growth is the Growth of the Identity Function
  16. Proposition: Infinitesimal Growth of Sine is the Growth of the Identity Function

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  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
  2. Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition