Khan Academy: Calculus: Polynomial Approximation of Functions (Part 4)

This video explores a listener's example of a function. You are given the composite function and one function, and you must find the other function.

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 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 relating the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series. [9:59]

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]