Khan Academy: Calculus: Polynomial Approximation of Functions (Part 6)

Video lesson finishing the derivation of the formula for the Maclaurin series and then applying it to find the polynomial approximation for e^x. [10:09]

Video lesson using a Maclaurin series to approximate a cosine function by using a polynomial function. Generalizes the expansion of cosine using sigma notation. [9:59]

Video continues a discussion about the relationship between the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series and uses those to derive Euler's formula and Euler's identity. [10:18]

Video lesson showing how to approximate a function at 0 using a polynomial by deriving the first three terms for the formula of a Maclaurin series. [9:45]

Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function. Generalizes the expansion of sine using sigma notation and relates it to the expansion for cosine. [9:24]

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 demonstrates how to write a polynomial that represents the difference between the area of a rectangle of given length and width and the area of a circle with a given diameter. [4:37]

Demonstrates how to write a polynomial expression for a given situation. [1:24]

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. [6:10]