Khan Academy: Calculus: Visualizing Taylor Series Approximations

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 showing how to approximate a function at any value using a polynomial by deriving the formula for a Taylor series. [7:27]

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 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]

Approximating a function at 0 using a polynomial

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

Video shows how to find the first four nonzero terms of a Taylor series of cos x. Also shows how to combine Taylor series for parts of a function to create a Taylor series for the entire function. [9:59]