Did two warm ups, dealing with order of operations and the mean value theorem. Went through syllabus in detail, including content, supplies, daily procedure, and the grading system. See here for more details on the grading system. Passed out reading assignment.
Notes from board
Homework
Complete reading assignment: digital copy
Pay $5 math fee: link
Have parent complete survey if needed: LINK
Warm up dealt with writing the equation of a line from 2 given points using point-slope form and sketching a parent function (absolute value, in this case) under 3 different transformations. Then discussed what a function is specifically, and how functions have different behaviors. Talked about what it means to be "close" to a number (could be close from 2 different sides, less and greater than) and then introduced the notation regarding limits with some color coding.
Did our first limit using direct substitution, then tried it on a rational function which led to zero divided by zero. Factored and canceled the rational function which led to a sensible answer. Also examined this problem with a graph and investigated numbers near the number we're looking into. Passed out a little graph and answered 8 limit and limit-related questions about the function from the graph.
Notes from the board
print out of graph added to notes
Homework
p. 55 #17-24
p. 67 #41-50
see calcchat.com for odd numbered solutions worked out
Resources
problem similar to warm up: writing equation and using transformations
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 dealt with remembering the unit circle in depth. Shared some shortcuts and soh-cah-toa level trig to help remember how certain patterns emerge. Went over homework, then used white boards to sketch graphs of functions that met certain criteria regarding limits and function values at certain points. (The notes below have links of all 4 examples we did, but each could have many many different answers.) Then looked back at the algebraic approach to limits and added a new tool to our toolkit, that of rationalization by multiplying by the conjugate. Worked one example as a class, then started one individually but ran out of time (it is completed in the notes below--final answer is -5/8). Handed out more practice with graphical limits.
Notes from board
Homework
- p. 67 #51-56
- #1-15 on this handout (digital copy)
- Assessment is Wednesday during DS (be able to: find limits by direct substitution and factor/cancel (could include trig, no calculator!), find limits using a graph)
Resources
another way to remember the unit circle: link
sketching a graph to meet limit criteria (like whiteboard activity) link1 link2
limits by rationalization: link
another rationalization example: link
some review on reading limits off a graph: link