AP: Test on limits.
Homework: none :)
Wednesday
AP: discussion of limits test
Homework: error analysis for test; finish multiple choice AP packet
Honors: Understanding continuity; establishing the 3 criteria needed for continuity; the 3 type of discontinuities; finding limits at discontinuities by factoring+canceling and rationalizing the denominator; evaluating one sided limits that go to infinity.
Notes from lesson
Homework: Worksheet
Thursday
AP: We launched class by exploring these "Good Questions" which are conceptual approaches to calculus and change: here is the handout
We then reviewed the multiple choice AP questions, brushing up on our limit skills that were assessed on Tuesday's test.
As we finished up limits, we introduced these special limits to memorize:
lim(x->0) of (sinx)/x = 1
lim(x->0) of (1-cosx)/x = 0
See this video for applications of these limits.
We then discussed continuity over an open interval and on a closed interval, which are extension of the 3-part idea of continuity at a point (the two roads meet at a bridge). Here is a resource to help you review continuity: link
We now understood what it means to "discuss continuity": most functions are continuous over the real numbers, with special exceptions made for their discontinuities (which are either jump, removable, or infinite). Remember to justify with limits your classifications of each one; for example, a removable discontinuity occurs at a point a where the limit approaching a exists, but does not equal the function at point a (which may be undefined).
We then introduced the idea of differentiation which is the limit as delta x (from the Algebra I idea of slope) approaches zero of the slope function (delta y over delta x). Here is a video summarizing that:
Homework: multiple choice worksheet
read section 2.1 from textbook
Friday
AP:
Homework:
Honors:
Lecture notes
Homework: p85: 5-7, 9-17, 29, 53-57