In this lesson I present several new topics connected with function limits – one-sided limits, cases where a function limit does not exist at all, and finally the notion of function continuity itself. I’ll show what to do when a function has no limit at all. You’ll see that continuity problems are usually the easiest limit problems – and why that is so.
This lesson lasts one hour and I work through 20 step-by-step examples (including parameter-based ones).
Table of Contents:
- introduction to one-sided limits of functions – 3 examples [01:37]
- one-sided limits (including an example with absolute value) – 3 examples [12:47]
- one-sided limits (with exponential functions) – 3 examples [19:47]
- limit as x approaches minus infinity – example [25:04]
- more difficult one-sided limits – 2 examples [30:04]
- introduction to continuity of a function – 2 one-sided limits [36:37]
- condition for continuity of a function at a point [39:39]
- continuity of a function at a point – example 1 [43:14]
- continuity of a function at a point – example 2 [46:09]
- continuity of a function at a point – example 3 [48:22]
- continuity of a function at a point – example 4 [53:11]
- continuity with a parameter – problem 1 [56:00]
- continuity with a parameter – problem 2 [58:38]
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)“
- “Two kinds of discontinuity points (function limits)“
- “What to do when the limit of a function does not exist?“