In this video, we review the concepts of factorials and equations of tangent lines to introduce the concept of using a Taylor polynomial to represent or approximate a transcendental function. Duration: 10:24

As requested, here are the mathematical experts at Numberphile to explain why 0! equals 1. Duration: 7:35

In Example 1, we extend the technique of writing the equation of a tangent line to a curve to writing a tangent quadratic, which is essential a second-degree Taylor polynomial. Duration: 11:50

What, a tangent parabola was not accurate enough for you? Then try this tangent cubic, which is a third-degree Taylor Polynomial. Duration:8:29

Okay, one more time, and I think we'll have enough evidence to generalize how to write a Taylor polynomial without having to generate and solve an obnoxious system of equations. That final piece of evidence is Example 3, where we construct a 4th-degree Taylor Polynomial. Duration: 8:11

Perhaps you noticed those factorials emerging as we took derivatives of our approximating polynomial. This video will formalize the process involved in writing either a Taylor or Maclaurin Polynomial. Duration: 13:58