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
