Video lesson using a Taylor series to approximate e^x around x=3 by using a polynomial function and then showing some of the graphs of the expansion by using the Wolfram Alpha website.

Approximating a function at 0 using a polynomial

Rationale for Euler's Formula and Euler's Identity

Understanding the properties of the remainder or error function for an Nth degree Taylor approximation of a function

Approximating f(x)=cos x using a Maclauren Series (special case of a Taylor series at x=0)

Video uses a property of the error function for a Taylor series expansion from a previous video to bound the (n+1)th derivative of the error function. Result is the Lagrange error bound.