Session 8: Limits of Sine and Cosine

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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

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» Clip 1: Limit of sin(x)/x (00:05:00)

» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Limit of (1-cos(x))/x (00:04:00)

» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Questions and Answers (00:11:00)

» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 4: Derivative of sin(x), Geometric Proof (00:12:00)

» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

The Function sinc(x)

 

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