- I'm collecting 11.1 homework today.
- I've finished grading your on-line homework for 9.1.
- I'm grading your 9.4 homework (sorry, not quite finished yet). A
couple of comments:
- Your "polynomials" have to be polynomials!;) You can't have square root functions, etc. playing a role. All those derivatives are evaluated at the abscissa about which you're doing your expansion (x=a).
- To find out where the two curves intersect (#2), you could use Newton's method (using the "solve" command in your calculator is equivalent):
- Once you've got a polynomial expanded about a, in terms of (x-a), don't expand those out! You're wasting time, and losing sight of the fact that we want to know what's going on right around a -- when (x-a) is small.
- As I said yesterday, I'm sorry that the discussion of #8 didn't resonate more with you. I prepared/am preparing a couple of pages that talk about some of the issues. You might want to check out the following:
- concerns several different means of testing for convergence of
series with all positive terms (obviously, if we're dealing with series
of all negative terms, similar results are going to apply).
- We're not so concerned with the actual limits (that is the values
of the series) as we are with the convergence (or divergence) of the
series.
- Theorems:
Theorem 3 is just a corollary of Theorem 2, where the integrals are the obvious power functions:
This theorem says that, in the long run, one series has terms which are simply a constant times the terms in the other series.
- Examples:
- Integral Test: #9, 10, p. 563
- Comparison Test: #20, p. 563
- Limit Comparison Test: #34, p. 563
- Divergence of the harmonic series (and dominoes!)