Hello errybody!!
Well, before we got started, Mr OB wasn't here, and then we realized that half the class wasn't here because they have a nordic race. Jealous!! Have fun and gooooood luck!! I hear we are supposed to get like 30 inches of snow on Friday so hoppppefully we have a snow day YAY!! and then we don't have to take the quiz... :)
^^THIS is some good news.! :D
This really isn't photoshopped, we are getting an ULTIMATE BLIZZARD named Nemo. Just keep swimming everybody!
This is how I feel to start off the class:
http://www.youtube.com/watch?v=Co0tTeuUVhU<---- that is Mr. OB for making me the scribe post.
IW's 4-8 are due on Friday
We have a test on February 14, which is VALENTINE'S day, which is also the day after the Passion Pit/ Matt and Kim concert in Portland which is ALSO the day before the Valentine's day dance and the hockey game and basketball game and February break. Anyways, not to clog your brain up, but we have a test on that day!!
The February break assignment is not mandatory, but if you want to get a five on the test, then you should try to think of it as an assignment. Supercorrections on the test will not be due until after February break.
OKAY. So once OB checked in with Eddie about his IW's, and named me as scribe, and also redeemed the CHILLS b-ball team for being cool again (who knew he had a secret grudge against Connor and Alex this whole time..) we got started on some WORK.
Goals:
Know and LOVE (<3) the FUNdamental Theorem of Calculus! Prepare to be excited.....
Page 297 Quick Quiz for AP Preparation: SEctions 6.1-6.3
1.
2.
3.
Memorize the list of properties on page 289!
After going on Geogebra and creating a graph of y=x^2, then setting a point A, then using the integral function of Geogebra, we made a conjecture based on our graph and our tracings. Make sure when using the integral function of Geogebra to use this one (there are multiple options after you type in Int):
Okay! So after we played with the graph, which looked like this:....
We found that as we moved point A on the x-axis, and traced the value b, it showed up to be the derivative of the graph which we originally put on there, which was y=x^2. Duncan so cleverly noted this as he told us that the graph of g was 1/3x^3 – 1/3.
THEREFORE
OUR CONJECTURE:
g(x) is an antiderivative of f.
If that is the case, we should be able to prove that. So here we go!
PROVE:
g(x) is an antiderivative of f(x).
In this proof, we used some of the rules stated on page 289, which I took a picture of and posted it above. Those rules include the subtraction rule and the mean value theorem. Here is a picture from the book showing the Mean value theorem for integrals:
By using the mean value theorem, we are able to determine that the derivative of g is f.
That is the first fundamental theorem of calculus. And it IS fun!
Fundamental theorem of Calculus, Part 1
Fundamental Theorem of Calculus, Part 2
And with that, the clock struck 12:50, so onto channel 30 we go. Remember, quiz on Friday and IW's 4-8 are due!
For the 40 minute period, OB started talking to us about the quiz which we were able to Supercorrect. He went over part C and D of the problem, and how most people got part C but missed part D which shouldn't have been the case! Because part D is easier than part C.... but then he went over the problems and found some loopholes and realized that part C is really simpler than part D. So don't take it hard on yourselves, this is TOUGH math!..as long as you're not Cole or Crockett!
Anyways, he suggested that we use our snow day to catch up on some work that we may have been slacking in so we be prepared for the quiz on Monday. Remember, Patrick JMT and Kahn Academy are your friends. Mr. OB will also still post IW#10 so try to get a chance to look at that! IW's 9-11 are due on Thursday, February 14.
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