In this lesson I introduce the concept of limits of functions (so far we dealt only with sequence limits). I show what is new and review the methods you already know – all of which can still be used for functions.
Note: Although the title says “simple”, the simplest function-limit problems can turn out to be the hardest – and I’ll show you how to defend yourself against that.
This lesson is 33 minutes long and I explain the topic through 12 examples.
Table of Contents:
- explanation of what a function limit is [02:08]
- function limits – 6 basic examples [04:03]
- factoring out the highest powers in function limits – 3 examples [14:55]
- multiplying by the conjugate in function limits – 3 examples [20:33]
- limit resulting in the number e – example [27:45]
Dubbed Version (Krystian AI):
AI Voice-over Version:
Original Version with Subtitles:
Formulas needed for the Lesson
Download trigonometric tables (PDF)
Homework
Download Answers to Homework (PDF)
Articles and blog posts related to this Lesson
- “Limit calculator (single-variable functions)“
- “Showing that sin x has no limit as x → ∞“
- “Function limit by substitution“
- “Limits of functions – Heine’s definition”
- “Limits of functions – Cauchy’s definition
- “Proving from the definition that a number is (or is not) the limit of a function”