1. Taylor Series Part 2

2. The power series that converges to f (x) can be written as…
If a series is centered at a number other than 0, then the Taylor series can be written as…
This is called the Taylor Series for f (x) centered at x = a.

3. Wait! Find the MacClaurin Series for ln x.
We can’t because ln x is not even defined at x = 0.
What ever shall we do?
We can find the Taylor Series centered at x = 1.
Now generate terms

4. So the Taylor Series for ln x centered at x = 1 is given by…
Use the first two terms of the Taylor Series for ln x centered at x = 1 to approximate:

5. So the Taylor Series for ln x centered at x = 1 is given by…
Find the maximum error bound for each approximation.
Wait! How is the actual error bigger than the error bound for ln 0.5?

6. To be continued…
This will lead into erroranalysis for error bound