- Just a note that there is now a link to section summaries off of the homepage:
- Your second assignment is returned.
- 12: two questions:
- Did you graph it on your calculator? (You should have, to check your work.)
- Did you just graph it on your calculator (then you missed the spirit of the problem).
- 70: Did you graph it? Did you check your derivative calculations?
- The solve button
- 78: Did you graph the family?
- Integrals (didn't grade these): noticed that some of you
aren't doing u-substitution correctly
- The integrate button
- 12: two questions:
- One more example:
- #68, 410
- We should spend a minute recognizing that we can turn any
exponential or logarithm of base b into another with base
e:
- We also want to realize that the natural log, ln(x), as the inverse of an increasing function, e^x, is also increasing; but, using the mirror, the increase in the exponential function, being extremely rapid, is reflected as an extremely slow growth in the natural logarithm.
- This section features the logarithm taking care of some tricky
cases that we couldn't handle previously, through a process called
"logarithmic differentiation" (which I outline in the highlights for this section).
Let's see this process in action, on an interesting function: the example 16, p. 417.
This section also introduces us to a few more ways of thinking about some complicated functions and their derivatives, and we'll look at some others.
- #47, p. 419
- 13
- 37
We'll end by looking over this lab: Logs and Exponentials as Models