Khan Academy: Calculus: Generalized Taylor Series Approximation

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. [6:38]

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

Video lesson showing the formula for a Taylor series expansion to five terms and uses it to approximate the cosine function. Includes the graphs of a specific number of terms of the approximate function using a graphing calculator. [18:05]

Video lesson using the Wolfram Alpha website to show the graphs of the Maclaurin series expansion of the sine function, demonstrating that approximations with more terms are better approximations of the sine curve. [6:01]

Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function. [6:33]

Video lesson using a Maclaurin series to approximate a cosine function by using a polynomial function. [5:37]

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

Video shows how to calculate the Lagrange error bound for a Taylor series polynomial approximation. [11:52]

Video first reviews the formula for a Taylor series expansion and then defines the error function to be the difference between the polynomial approximation and the actual function. Properties of the derivatives of the error function are...