AP: Went over sample test, reviewed rationalizing the numerator to allow for direct evaluation of limits. (See video HERE for review.) Then discussed asymptotes, which can be redefined as limit statements:
Honors: In DS we discussed the first homework assignment on numerical and graphical limits, which mostly went well. Then in class we started to examine "direct evaluation" of limits which allow us to understand that some functions behave near a given value very similar to how they evaluate at that given value--such functions are called continuous functions. Even if the function is not continuous or defined at a the given value, direct evaluation can help reveal behavior approaching the value.
Here are the notes from today's class
Homework: Worksheet (due Wed)
Tuesday
AP: Discussion of homework; properties of limits to assist in direct evaluation; intuitive understanding of Intermediate Value Theorem (remember: continuity is a precondition for it to apply);
Notes from Tuesday lecture
Homework: p78: 75-78, 95, 100-103 (due Wednesday)
Wednesday
AP: In DS, we demonstrated some practice problems relating to the Intermediate Value Theorem and introduced the next topic to consider after Limits, the rate of change (and finding instantaneous rate of change). Notes from lecture
Homework: average rate of change
Honors: Journal on asymptotes as limits. See images above from AP on Monday for the formal definitions. In-depth discussion of homework solutions, involving the evaluation of limits; introduction of concept of continuity and how it makes it useful for direct evaluation (since the values "close" to a given number are also close to the function evaluated at the given number itself). This idea of direct evaluation also unlocks many useful and easy properties, which we looked at. The chart on p. 57 is particularly useful as a reference. Lecture notes
Homework: front side of this wksht on Direct Evaluation
Thursday
AP: First Test is Coming Up On Tuesday!!! Study Guide (here) (IMPROVED STUDY GUIDE WITH SOLUTIONS, ETC LOCATED HERE)
Practice with this image for generic curve graphical understanding of limits
Test is free-response and no calculator; approximately 25 questions.
Practice multiple choice test handed out at end of class; see (here) for solutions
Friday
Honors: homework: p65 37-44 ; p 76: 7-12, 25-28