We started class watching ViHart’s video discussing the validity of tau rather than π to measure radians. From that we watched an incredibly confusing video about digamma or wau. This is really hard to comprehend until you find out that wau is really just one. This video of wau was just one huge pain in the ass.
Next, it was time for the really difficult IW quiz.
OB's naughty list: Elazar, Alex, Weston, Eliot, Connor, Lexi, Noah, Cooper, Megan, Francie
OB's explanation of the calendar:
Submit IWs by thursday because OB will be gone so the zero of the missing assignments will sit there for a long time. Over the weekend the assignment is to finish up IW 5. The answers to IW 5 will be posted sometime soon. IW 6 and 7 will be free response questions. OB predicts that we'll have about 3 hours to work on 6-7 free response problems. All of the answers will be available online. The next quiz will be Friday 3/22 and will include questions directly from IWs 6 and 7. There won't be any notes or blog post, but if you do these problems the quiz will be like free points. These questions will also be on the test in two weeks. OB wants us to take them seriously. According to OB we’ll have about 3 hours to do 6-7 free response questions. All IWs and supercorrections will be due by the end of the quarter which is three weeks away. 4th quarter starts with a follow up test. There will be two quizzes before spring break. These quizzes will cover multiple choice and free response questions from the IW. There will be extra credit available over spring break. In April 2 quizzes right before spring break. they will be MC and free response AP questions from old IW. Extra credit will be available over spring break. After spring break we will take a full AP exam. OB recommends we do the IWs to simulate the test. After May 8th we have a project which will last nearly a full month. No IW after may 8th! Less than two months until the end of AP Calculus! We are about 57 days from the AP test.
Onto IW 5, we did problem 31 from page 411. This set of problems is question 4 on IW 5. Problem 31 part a starts off by finding the volume of the shape enclosed between the y-axis, y=x^2, and y=1. If you have been doing your IW this week 31 shouldn't be too difficult, as long as you remember it's top - bottom. Part b has you find the area of the object when you rotate around an axis which the area isn't touching. This is difficult to imagine conceptually, remember that you need to subtract to volume between the area and the axis of rotation.
31. Find the volume of the solid generated by revolving the region bounded by the parabola y=x^2 and the line y=1 about
a) the line y = 1.
b) the line y = 2.
c) the line y = –1.
Here is a graph of the problem situation:
a)
b)
c)
Here is an interesting video covering a similar topic, but with a little more rewriting of the integrand.
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