Section Summary: 3.3

  1. Definitions

    Make a list of all definitions in the section (a few words each is fine). Summarize any lengthy definitions introduced in this section in your own words.

    Didn't notice any!

  2. Theorems

    Make a list of all theorems (lemmas, corollaries) in the section (a few words each is fine). Summarize each one introduced in this section in your own words.

    For the following, we assume that f and g are differentiable functions.

  3. Properties/Tricks/Hints/Etc.

    Make a note of any especially useful properties, tricks, hints, or other materials.

    ``The theorems of this section show that any polynomial is differentiable on tex2html_wrap_inline217 and any rational function is differentiable on its domain.''

    Examples:

  4. Summary

    Summarize the section in two or three sentences.

    This section is replete with formulas for some of the most important functions we will be working with (these formulas must be committed to memory!). It began with a few special cases, then began extending to general cases: several of these follow our intuition, e.g. the sum rule (the derivative of a sum is the sum of the derivatives); others are not so intuitive (the product and quotient rules are not obvious). There were many examples which demonstrated how one uses these formulas.

    Proofs are given for these special formulas, and, for the most part, are not too complicated. One proceeds directly from the definition of the derivative function as the limit

    displaymath190

    and one hopes that things just fall out!

Problems:

Problems pp. 156-158, #4, 13, 17, 24, 32, 44, 60, 63, 80; Board: 3, 18, 16, 37





LONG ANDREW E
Tue Jan 30 22:49:36 EST 2001