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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

Select the first clip below to begin.

» Clip 1: Introduction to Linear Approximation (2 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Linear Approximation to ln x at x=1 (3 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Linear Approximation and the Definition
  of the Derivative (4 min)
» Accompanying Notes (PDF)

From Lecture 9 of 18.01 Single Variable Calculus, Fall 2006

» Clip 4: Approximations at 0 for Sine, Cosine and
  Exponential Functions (8 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

 

Comparing Linear Approximations and Calculator Computations

Lecture Video and Notes

Video Excerpts

Select the first clip below to begin.

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

 

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