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In this lesson I show how to transform various limits so that they match the most common formulas with sines, logarithms, etc.
You’ll learn many simple tips for steering a limit toward the right function-limit formula.
This lesson lasts 47 minutes and I walk through 19 different step-by-step examples.
Table of Contents:
- limit formulas for functions [01:17]
- limits using formulas with sin x, tan x, arcsin x, arctan x – 6 examples [05:39]
- limits using formulas with exponential and logarithmic functions – 4 examples [15:12]
- limits with sin x and transformations – 2 examples [20:10]
- limit using the cosine-difference formula – example [22:57]
- formula for the limit with cosine [26:31]
- limits with more difficult transformations – example 1 [28:25]
- limits with more difficult transformations – example 2 [31:25]
- limits with more difficult transformations – example 3 [35:10]
- limits with more difficult transformations – example 4 [38:00]
- limits with more difficult transformations – example 5 [40:50]
- limits with more difficult transformations – example 6 [42:58]
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)“
- “A useful function limit with cosine“
- “Limit of the function sin x / x – proof”