In this video we are going to talk about linear approximation to functions. The idea here in geometric terms is that a curved line can be approximated by a straight line tangent to it. Of course, this approximation is only good near the point of tangency. First, we are going to see some essential equations that will be used in the following examples. The most important one is formula of the line tangent to the curve at x=a. We will draw a simple graph to illustrate this. Then we will talk about df and Δf and see what do these terms mean.
This amounts to
finding the equation of a tangent line.
If your instructor
uses differentials, familiarize yourself with this notation.
Work through the
geometry of linear approximation and of differentials.
You will probably
be asked to use the linear approximation to estimate the value of a
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.