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

Fall 2010
##### Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Simulations
Recitation Videos