(Wednesday after Test 2)

Topics:

• Taylor’s Theorem and the error term

• The Mean Value Theorem and Rolle’s Theorem (Ch. 3 section 3.2)

Here are my notes on the examples I used to illustrate these theorems:

MAT1575MeanValueThmRollesThmillustrations

You can also view this video on the MVT from PatrickJMT

We will use the Mean Value Theorem to prove the error term in Taylor’s Theorem, and then use the error term bound to figure out how many terms of the Taylor polynomial we would need to make the error be less than a specified amount.

Homework:

• Review the examples discussed in class

• Do the WeBWorK:

• There are no problems in the textbook assignment on the Mean Value Theorem, so make sure that you do that assignment on WeBWorK!

• For extra practice on Taylor polynomials you can do the problems p. 475 #5-20

• No quiz next time.

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!