Session 23: Linear Approximation

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Overview

Linear approximation is a powerful application of a simple idea. Very small sections of a smooth curve are nearly straight; up close, a curve is very similar to its tangent line. We calculate linear approximations (i.e. equations of tangent lines) near x=0 for some popular functions; we can then change variables to get approximations near x=a.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Introduction to Linear Approximation (00:02:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Linear Approximation to ln x at x=1 (00:03:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Linear Approximation and the Definition of the Derivative (00:04:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 4: Approximations at 0 for Sine, Cosine and Exponential Functions (00:08:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

 

Comparing Linear Approximations and Calculator Computations

Lecture Video and Notes

Video Excerpts

Flash and JavaScript are required for this feature.

» Clip 1: Approximations at 0 for ln(1+x) and (1+x)r (00:03:00)

» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

 

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