No school Monday for eclipse. Went over homework in DS on graphical and algebraic limits, then did some practice problems. Warm up involved more algebraic limits, sometimes of linear functions. Passed out first quarter learning targets, then took first assessment and briefly looked at properties of limits (mostly common sense). Then saw that 0.99999..=1 and talked about what asymptotes really are and how to define them. Introduced a new approach to limits that cannot be factored or rationalized, which involves taking a one-sided limit and plugging in representative numbers to see behavior tending toward zero or infinity. Defined both vertical and horizontal asymptotes in terms of limits producing and limits approaching infinity, respectively.
Notes from board
First Quarter learning goals
Homework
p. 88 #13-20, 33-40 [had to modify it from what was on board]
Resources
find vertical asymptotes of a function (video made by me!!) link
one sided limits (helps with #33-40) link
more one sided limits link
Passed back assessments, went over homework, then did warm up involving a limit at a variable and special factoring. Looked back at horizontal asymptote definition and (re)developed rules for how to find them in cases of rational functions by taking limits at infinity. Worked through 2 examples regarding finding and justifying the locations of horizontal and vertical asymptotes for a given rational function.
Notes from board
Homework
Complete practice assessment (skip #2 for now) [blank copy] [SOLUTIONS]
Real assessment is on Wednesday during DS
Resources
algebraic approach to horizontal asymptotes/limits at infinity: link
find vertical asymptotes of a function (video made by me!!) link
one sided limits link
more one sided limits link
finding asymptotes with limits: link