- Major/Minor Lunch Friday, October 3 from 11:30am-1:30pm in ST 343.
- Section 8.6 problems are due today.
- I'm returning your 8.1 problems (off-line problems)
- Why is K4=16?
- Tell me: What's the point of this exercise?
- Would those who presented test problem solutions in class please return their tests to me, so that I might scan the solutions and make them available to others? Thanks!
- What kinds of problems are we looking at in this section? Arc
length and surface area calculations for areas of revolution:
- Let's start with arc length:
The usual trick is to discretize something continuous, and then pass to a limit:
Now hopefully we can figure out how the formula will look:
So what's the general formula?
- For surface area (for areas of revolution)
We discretize bits of the surface, and then make a series of little bands; take the limit, and get the general formula:
- Examples:
- #39, p. 476
- #51, p. 477
- The big picture: we're approximating nasty functions with nice ones (polynomials):
- Taylor Polynomials Lab (p. 213 of Stewart's Calculus)