Section 12.12 Worksheet:

Assignment: Exercises pp. 806-808, #8, 18, 19, 30 (due Tuesday, 4/27).

1. In what ways can we use the Taylor series to estimate the size of the errors we're making in approximating a function with a Taylor polynomial of given degree?

2. In the optics example described at the end of the section, what motivated Gauss to make his approximation?

3. What is the ``punch line'' of Example 3, concerning Einstein's theory of relativity?

4. You've already seen Example 2: we did it, only using a polynomial approximation of degree 7. Explain (again!) why only odd powers of x appear in the Taylor series for .

5. In which example is a binomial series approximation used?