Worked through a challenging task of simplifying an expression. Went over the syllabus in some detail. Started looking at Mr. Frumble, a character who helps us understand calculus concepts.
Notes from board
Homework
Watch this video from 01:30 to 10:00 (watch all of it you like it!): link
Warmup was another challenging simplifying expression task. Thought about how to find your speed at an exact instant in time if your speedometer were broken but you had a watch and could count miles. Involved taking the old formula of rate = distance/time and using function notation to represent the change in distance over the change in time. The change in time, however, would need to be 0, which leads to the conundrum of dividing by zero. Instead, we use a limit to approach zero. This brings us to the limit, which we first decode then understand as an operator and as an output. We then solve our first limit through direct substitution, then see that this method fails for some problems. This leads us to look at the the graph and try numbers getting close to our target. Then with "factor and cancel" we can algebraically extract the answer. Started looking at limit nonexistence which is when a function does not approach the same value when approaching an input from left and right.
Notes from board
Homework
p. 55 #17-24
p. 67 #41-50
see calcchat.com for odd numbered solutions worked out
Resources
what is a limit: link
finding limits from a graph (helps with p55) link
finding limits by factoring and canceling: link
bunch of worked out examples: link
Warm up was to fill out an entire unit circle. Shared some strategies to help with this, limiting what one has to memorize. Went over homework in depth, then practiced some more with limits from a graph, then did graphical limits involving infinity on a generic graph without numbers. Started looking at rationalizing to solve limits.
Notes from board
Homework
p. 67 #51-56
First assessment: 8/23
Resources
another way to remember the unit circle: link
limits by rationalization: link
another rationalization example: link
some review on reading limits off a graph: link