Lecture 19 - Linear Approximations and Differentials

In this video we review the idea of using the tangent line to an equation to estimate the value of this equation for values close to the x-value of tangency. We call this tangent line the linearization of f(x) at x=a.

After this we introduce notation for the differential and talk about the meaning of delta x, dx, delta y, and dy. We work through a few more example problems, one finding all of these quantities and another where we use the differential to estimate maximum possible error.