Warm up: written response to "A Mathematician's Lament."
Discussion of what a function is, began to look at the notation for a limit and how to use it and what "closeness" means in mathematics. (F-LF1, F-LF2). Handout that we will look at in more depth Wednesday. Lecture notes.
HW (due Friday) : p. 55: 17-28, 66, 71, 72 (alignment: F-LF2a)
Resources: good demonstration of numerical and graphical concept here: https://www.youtube.com/watch?v=riXcZT2ICjA
Warm up focused on a domain of a function and a discussion of continuity and also using a limit. Continued introduction of limit, talking about limit existence, one-sided limits, how to find limits for "well behaved" functions (just plug in the value) and also limits when a function has a "hole" in it. Also looked at graphical approach by using generic graphs. Lecture notes
Homework: same as last class, due friday. See Calcchat.com for odd numbered solutions
Warm up on determining limits from a graph. Went over homework on graphical limits. Some questions on how to draw a graph meeting certain criteria. Learned about algebraic approaches to finding limits, including direct substitution, properties of limits (mostly common sense), composite functions, special trig limits (very important!!), and also the process of factoring to cancel out ("massaging") and also rationalization. (F-LF1) Lecture notes
Homework: p. 67: 6-30 (multiples of 3), 40, 52-54, 65-67 (aligns to F-LF1)
Resources:
Limits from a graph:
https://www.youtube.com/watch?v=aVcqrDFcaCA
https://www.youtube.com/watch?v=UkjgJQaGx98
Limits analytically:
https://www.youtube.com/watch?v=MspClN-r8C0
Trig limits:
https://www.youtube.com/watch?v=mp94QNJ9aCc
https://www.youtube.com/watch?v=orBS7XfSOag