Khan Academy: Calculus: Polynomial Approximation of Functions (Part 2)

This video continues to look at evaluating functions by looking at examples of evaluating basic composite functions.

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 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]

Watch a video to explore part 2 of Green's Theorem.

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]

Sal analyzes the limits at infinity of three different rational functions. He finds there are three general cases of how the limits behave.