- Official Calculus Lab Hours
- Section 7.2 homework problems are due next time, Friday.
- Your assignment for section 7.3 is to be completed on-line: please do that before next Tuesday. pp. 364-366, #4, 9, 10, 11, 14, 19, 21, 22, 28, 32, 51, 60, 64, 79, 85, 103
I'll be taking your grade from your work on-line, while watching your attempts. Important Note: when you need to use the absolute value function, write abs(x) (rather than |x|. You basically input functions just like you would to your TI calculator. I believe that the software checks your answer by comparing it numerically on a bunch of points on a given domain.
- Let's start by thinking about some real-life problems that would
require the use of the inverse of an exponential function.
- From science?
- From business?
- From mathematics?
- Logs are, by definition, the inverses of the exponential functions:
- The laws of logarithms are reflections of the properties of
exponentials:
- The derivation of the derivative of the natural log function is
easy, given our work on inverses:
- Another way to define the log function is as the anti-derivative
of the "weird power" x-1:
(How does symmetry help us to understand the absolute value in this result?)
- Examples:
- 1-3, 5-8, p. 364
- 15-18, 20, p. 364
- 45-50, p. 365, and draw!
- 80, 86, 94, p. 365
- 108, p. 366
- 109, p. 366
