Khan Academy: Maclaurin and Taylor Series: Euler's Formula and Euler's Identity

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. [6:38]

Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function.

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

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.

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

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]

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]

Approximating a function at 0 using a polynomial