9.2 day 2

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# 9.2 day 2 - PowerPoint PPT Presentation

9.2 day 2. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Finding Common Maclaurin Series. Liberty Bell, Philadelphia, PA. Maclaurin Series:. (generated by f at ).

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9.2 day 2

Photo by Vickie Kelly, 2003

Greg Kelly, Hanford High School, Richland, Washington

Finding Common Maclaurin Series

Maclaurin Series:

(generated by f at )

There are some Maclaurin series that occur often enough that they should be memorized. They are on your formula sheet, but today we are going to look at where they come from.

List the function and its

derivatives.

Evaluate column one

for x = 0.

This is a geometric series with

a = 1 and r = x.

We wouldn’t expect to use the previous two series to evaluate the functions, since we can evaluate the functions directly.

They do help to explain where the formula for the sum of an infinite geometric comes from.

We will find other uses for these series, as well.

A more impressive use of Taylor series is to evaluate transcendental functions.

Both sides are even functions.

Cos (0) = 1 for both sides.

Both sides are odd functions.

Sin (0) = 0 for both sides.

and substitute for , we get: