Overview
When we tried to differentiate the sine and cosine functions we were left with two limits to calculate. In this session Professor Jerison calculates these limits, taking a close look at the unit circle and applying some fundamental ideas from linear approximation.
Lecture Video and Notes
Video Excerpts
» Clip 2: Limit of (1-cos(x))/x (00:04:00)
From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006
» Clip 3: Questions and Answers (00:11:00)
From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006
» Clip 4: Derivative of sin(x), Geometric Proof (00:12:00)
From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006
Clip 4: Derivative of sin(x), Geometric Proof
> Download from iTunes U (MP4 - 110MB)
> Download from Internet Archive (MP4 - 110MB)
Worked Example
The Function sinc(x)