In class on 10/28, we started off by Ms. Sommariva showing us some some tips of how to use the N-spire calculator. There are certain functions we didn't know about that would be helpful for us to check our work. For example, we learned that we can type in a function and it will give the factors for us. Also, we completed a problem in the notes packet where we were trying to foil a expression to the 4th power. In this case, we could use Pascal's triangle. The N-spires allowed us check our work by typing expression in. 

Ms. Sommariva showed us a quick powerpoint about derivatives and tangent lines with graph examples. 

We received a new notes packet and went over the chapter 3 test requirements, definition of derivative at a point, formulas for difference quotients and an example. 

We ended class by completing a short exploration. We practiced the definition of derivatives at a point concept we learned in the notes packet. 

Our homework assigned (due on 10/30) was to complete HWK 3.2 pg 76 Q1-Q10 #3, 5, 9, 15, watch this video http://www.youtube.com/watch?v=TINfzxSnnIE, and use the backwards or symmetric difference quotient to find the derivative of x^4.

-Kiley :)

IVT and Continuity examples

We will review the IVT and proofs of continuity in class on Tuesday when we are all back together. However, after looking at your work on the review stations, I wanted to share some of the work of your classmates. Here is a good example of the work expected when using the IVT:

Here is a good example of the work expected when proving continuity:

In class 10/15 we worked at different stations that had to do with limits. There were four stations that each had to do with a specific learning style. The "Understanding" station had the group go online and post everything that we knew about the key words in our unit like: limit, derivative, etc. The "Self Expressive" station had each member of the group write a letter to the author of our textbook saying whether we thought limits and continuity should be in the same chapter or not. The "Interpersonal" station had the group work together on solving the magic box. The "Mastery" station had us solving limit problems. All of these stations helped to reinforce what we have learned about limits and deepen our thinking about their connections with other things we have learned such as derivatives and continuity. After we finished the stations we were able to begin working on our homework, which was the back of the analyzing limits sheet.

Julia's Limit Example

Another Limit Example (with lots of algebra!)

Here is another limit example from the Magic Squares you did in class today. In order to solve this limit algebraically, you needed to use the difference of cubes and difference of squares for factoring.

Danny Schick's Limit Example

Maia's Example

Ethan's Limit Example

Dani Hart's Limit Example

Summer's Limit Example

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Josh's Limit Example

Jason Limit example

Ben Cross's limit example

Jeremy's Limit Example

Ethan Miller's Limit Example

10/11/13 Class reflection

Today in class, we started out with the daily problem which touched upon our understanding of definite integrals. After that, we went over the FRQ that had been assigned to us the class before (10/9/13). The first question of the FRQ just required us to use derivatives to figure out the rate at which the number of people waiting in line changed at 5:30pm. In part two of the FRQ, we had to use the trap rule to figure out a definite integral of the average number of people waiting in line during the first 4 hours that the tickets were on sale. As a reminder, the trap rule is as follows: 1/2(b1 + b2). In the third part of the FRQ we were asked to figure out the fewest number of times at which L'(y) must equal 0, and Ms. Sommariva had to walk us through this one because the IVT is a relatively new concept to us. After we went over the FRQ together, we moved onto the homework check. The homework check tested us on our understanding of limits and the IVT. After we finished the homework check, we took two concept tests, one on concept #3 (continuity) and the other on concept #4 (evaluating limits). This pretty much sums up what we did in class yesterday.

Daniel's Limit Example

I also had issues getting this post into a comment.  So I had to make a new post

Kiley's Limit Example

To do the limit assignment, you are going to have to make a new post because you can't insert Daum Equation Editor in a comment.

Daum Equation Editor Assignment

Your assignment is to make a comment to this post (not a new post) that uses Daum Equation Editor to show a limit example. Use limit notation to write the example and then make sure to evaluate it. You can also use each others' examples to study limits for your Chapter 2 test. This post is due by Tuesday October 15th.

Wednesday October 9th

Last class we started with a POD as usual. We then went over check 2.45 because many people had questions on the last problem. I don't have this to go over but there was a similar problem on the limits worksheet, so I will explain that. Exercise 5 on that worksheet said:

lim        (1+h)^4 -1                          0              1             
h--> 0           h                                  1            1 1
                                                         2          1 2 1
                                                         3        1 3 3 1
                                                         4      1 4 6 4 1   

1(1^4)(h^0) + 4(1^3)(h^1) + 6(1^2)(h^2) + 4(1^1)(h^3) + 1(1^1)(h^4)      substitute into function

(1 + 4h + 6h^2 + 4h^3 + h^4) -1                                         ones cancel, factor h out of polynomial
                         h

h(4 + 6h + 4h^2 + h^3)                                                                  h cancels, substitute to find answer
                   h

4 + 0 + 0 + 0 = 4 final answer

Basically you need to expand the polynomial in the numerator. when expanding anything more than the power of 2 or 3 it is easier and faster to use pascal's triangle. This is review from pre-calc but you use the triangle by looking at the row of the triangle that corresponds with the degree you are raising the polynomial to. Then for each number in the series you multiply the first value in the original polynomial to the highest degree (and in descending order as you move onto the next term) and the second value to the 0th degree which is always one (and in increasing order as you move to the next term). It may be easier to understand looking at the example above.
We also went over part two of the FRQ 2003 #6 which was a helpful to show how the AP wants the answer found when there is no calculator. Then we did the two part exploration. Finally we received our homework...

HOMEWORK DUE FRIDAY: the new FRQ 2008 #2 we got last class as well as check 2.5. No bookwork

Josh Gervais

Thursday 10/3/13

We started off the  class with a daily problem. Once finished, we moved into notes 2.4 We went over these notes that we had taken the night before to clarify any problems we had and to expand on what we wrote down slightly. We also took notes 2.45 on the continuity of piecewise functions, and boolean variables. In order to type in a piecewise function on a TI-nspire, go to your graphing window. When you are prompted to insert your function, press the button on the right side below the delete button and left of the button that has a book on it. In the menu on the screen, choose the one with the curly bracket, and four boxes. Then, type your first equation in the upper left box, and its restrictions to the right of it. Do the same with your second equation, except in the lower left and right boxes. To do this on a TI-83/84, go into y=. In Y1, type in your first equation in parentheses. After the equation, put a division symbol and the equations restrictions in parentheses after the division. You can get to the greater than, less than, and more symbols by pressing the math button. Do the same thing for the second equation, except typing it in Y2. We then answered any questions we had on the book work and the evaluating limits worksheet. We did check 2.4 regarding the concepts we have been learning and did an exploration regarding continuous and discontinuous piecewise functions. We finally finished up class with grabbing the FRQ and starting it if we had time.

Tuesday 10/1/13

Today in AP Calc. we started with the problem of the day about the open box, and writing the equation to find the volume of it.  Following this we completed the Homework Check 2.3 which involved finding delta values along with finding the limits graphically.  We then took some notes on finding the limit algebraically using either Substitution, where you can just take the x-value and plug it into the equation, Factoring, where you use synthetic division to factor the top of the function so that there is a similar term in the numerator and denominator that will cancel out.  You then do substitution to figure out the limit.  The third way is using Conjugate Method, which is only used if you cannot factor, which in most cases is when there is a square root.  With this you take the conjugate of the numerator and using the magic box, get it so that there is a factor in both the numerator and denominator that will cancel out.  You can then use substitution to find the limit.  We were then given the Limit Worksheet to begin our homework.

TONIGHT'S HOMEWORK: Finish Graphical Approach to Limits packet, #1-4 on the Evaluation Limits worksheet, complete the page 1 notes for 2.4, watch the two videos posted on the website, and finish HW 2.3 - p. 43 Q1-Q10 #10, 11, and 17

Hi

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