Khan Academy: Calculus: Taylor Series at 0 (Maclaurin) for E to the X

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 an exponential function by using a polynomial function and relates its polynomial approximation to that for the sine and cosine functions.

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]

Video uses a property of the error function for a Taylor series expansion from the previous video to bound the (n+1)th derivative of the error function. Result is the Lagrange error bound. [15:08]

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 shows how to use the Taylor series of a function which was found in the previous video to find the sixth derivative of the function at 0. [2:58]

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

Video shows how to write the first four nonzero terms of the Taylor series for a function. [7:42]

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 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...