We don't always build our Taylor series function by taking a bunch of derivatives. In the previous lesson, it was far easier to just manipulate a geometric series. Sometimes a function is also too complex to take a thousand of its derivatives. This video demonstrates how we can make a series with term-by-term multiplication... Duration: 7:11

...or through long division. Duration: 9:33

Example 8 mimics a free-response question in which you are writing Taylor polynomials based on a table of derivative values. Also, you might want to review your notes on the Lagrange remainder, just in case it comes up. Duration: 17:07

Apparently, it did come up, so let's take a moment to re-examine the Lagrange remainder before applying it to one last example. Duration: 14:37