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.

| | | | created: 2020-07-10 18:36:16 | modified: 2020-07-10 18:40:21 | by: bookofproofs | references: [581], [8311]

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