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
» Clip 1: Introduction to Linear Approximation (00:02:00)
From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Introduction to Linear Approximation
> Download from iTunes U (MP4 - 103MB)
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» Clip 2: Linear Approximation to ln x at x=1 (00:03:00)
From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Linear Approximation to ln x at x=1
> Download from iTunes U (MP4 - 103MB)
> Download from Internet Archive (MP4 - 103MB)
» Clip 3: Linear Approximation and the Definition of the Derivative (00:04:00)
From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006
Clip 3: Linear Approximation and the Definition of the Derivative
> Download from iTunes U (MP4 - 103MB)
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» Clip 4: Approximations at 0 for Sine, Cosine and Exponential Functions (00:08:00)
From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006
Clip 4: Approximations at 0 for Sine, Cosine and Exponential Functions
> Download from iTunes U (MP4 - 103MB)
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Worked Example
Comparing Linear Approximations and Calculator Computations
Lecture Video and Notes
Video Excerpts
» Clip 1: Approximations at 0 for ln(1+x) and (1+x)r (00:03:00)
From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Approximations at 0 for ln(1+x) and (1+x)r
> Download from iTunes U (MP4 - 103MB)
> Download from Internet Archive (MP4 - 103MB)