18.01SC | Fall 2010 | Undergraduate
Single Variable Calculus
Part A: Approximation and Curve Sketching

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

Clip 1: Introduction to Linear Approximation

Clip 2: Linear Approximation to ln x at x=1

Clip 3: Linear Approximation and the Definition of the Derivative

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

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

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Course Info
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Fall 2010
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grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations