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Session 24: Examples of Linear Approximation

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Overview

When using linear approximation, we replace the formula describing a curve by the formula of a straight line. This makes calculation and estimation much easier.

Lecture Video and Notes

Video Excerpts

Select the first clip below to begin.

» Clip 1: Curves are Hard, Lines are Easy (4 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Linear Approximation of a Complicated
  Exponential (5 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Question: Can We Use the Original
  Formula? (3 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Worked Example

 

Product of Linear Approximations

Lecture Video and Notes

Video Excerpts

Select the first clip below to begin.

» Clip 1: GPS Time Dilation Example (7 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Relative Error (3 min)
» Accompanying Notes (PDF)

From Lecture 10 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Recitation Video

 

Implicit Differentiation and Linear Approximation

 

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