Reviewed limits at infinity and infinite limits (asymptotes). Took an assessment.
Homework: none =)
Wednesday
Developed idea of continuity at a point by examining the analogy of roads and bridges. Arrived at definition of continuity at a point (3 conditions). Examined types of discontinuities: jump, removable, and infinite.
TIP: Jump discontinuities are usually piecewise functions, but piecewise functions can also be removable discontinuities. Infinite discontinuities typically occur when there is a term in the denominator that cannot be factored/"massaged" out. Removable discontinuities are usually of the type you can factor and cancel out ("holes"). (F-C1, F-C2, and F-C3)
Homework: p. 79: p. 79: 3,4,6,12,18,28,30, 39-54(x3), 61 ,62 (shared among F-C1 F-C2 and F-C3)
Resources:
types of discontinuities: http://faculty.bucks.edu/taylors/calculus/discon.html
http://www.math.brown.edu/UTRA/discontinuities.html
showing a function is continuous or discontinuous algebraically: https://www.youtube.com/watch?v=YOuiXpLqDr0
classifying discontinuities: : https://www.youtube.com/watch?v=NjyKv8oL1XM
note: "point discontinuity" is a removable one; "vertical asymptote" is interchangable with infinite discontinuity
Warm up on how to show continuity and classifying a discontinuity of a piecewise function. Went over homework. Worked on AP sample limit problems (handout here).. Will complete the multi-part problems next week. Multiple choice homework handed out (linked here) omit the ones with the x's next to them. (F-C1 F-C2 and F-C3)
Homework: AP problems handed out near the end of class (F-C1 thru F-C3)
Assessment on Wednesday: will cover continuity and discontinuities
bonus video: proof of e as a limit to infinity (will make more sense in a few weeks)