apr.27th/09

In today's class Mr.K went through the our wiki, to show us some tips to compare the difference between two person's edits of the question. All you have to do is to quick the page history, then choose the two that you wants and qiuck compare. The green parts are the parts that are added, and the red is the parts that are been deleated. Also the deline for DEV project is extened, due to the high purssre of the upcoming AP Exam.

As always we did a mini exam to help us review for the exam:
Q1/
Find the derivative of both function, which V1=cos(t) & V2=-2e^(-2t)
It's in terms of V because the X1 and X2 are the postion fungction the derivative of postion is velocity which is V.
Then you let V1=V2, which is cos(t)=-2e^(-2t). You can graph both is the calacror or find the interstion point of the two functions. OR you can let the whole thing equals to 0, cos(t)+2e^(-2t)=0
then find the root of the function. The answer should be D)three

Q2/
In this parblem you applie the derivative test rules. Graph the function, then find where the function have it's roots over the interval [-1,]3]. Then at the three roots find the point that is going from negative to postive, because it's a local minimum. Your answer should be E)2.507

Q3/
From the graph, take a slice and look at it as a disk with a washer in it. Then , cos(x)=x which becomes 0=cost(x)-x. use the area formular the pluge everthing in to find the function . If you done everthing correctly you should end up with C)1.520

Q4/
will this question camed up the third time, I think everyone is good with it. The answer is D)8647 gallons.



The end..............
Next scribe is Justus.

bob

BOB, again!!! Almost forgot to do it.
OK I went through the Chapter yesterday, everything seems to be easy and also hard.
I'm having trouble with most of the word problem question.
In this unit you always have to think through the whole question and find the giving data.
It's really easy to miss some parts.
OK I have to o back to review now, good luck everyone!!!

Scribe again!!!!!
OK, we start with finishing the honeybee problem. To be honest I didn't really get it, it's kind of hard for me to understand. I will skip that question.

Then we went to the quiz, parties exam questions.


In this question you use 2ND derivative test to find the concavity of the original function.
I will use Mr.K's work

red part is the 1st derivative, then he used green to find the 2ND derivative .
After that he use the number line to complete the 2ND derivative test.


For this question there isn't any correct answer for it,I will explain it any way:



A graph will help to find how the triangle look like on the graph.
Use the area equation: 1/2bh then find a(3) =54, because the coordinates of the triangle is (x, 27-x^2) use it to build the area equation. Then use the first derivative test to find the max and min, evaluate the area from then.



This is the mean value question that we have to use the formula
to help us to find the answer.
1st we plug the values in to simplified it then evaluate it from 0 to pi/3.
Find the anti-derivative of tan(x) by using substation. If you done every thing correctly the answer will be B.



i picked A for this one and I think I'm not the only one who gets wrong on this question.
It's not as easy as I thought.
We forget the dx part that it counts as part of the substation.
That's where the 1/2 comes from, u find dx to replace dt, because x is use to replace 2t+1.
Then you work thought that you should end up with D.

Mr.K will be away tomorrow and the next couple days, someone else will be here for him but he doesn't know who.

Next scribe will be...paul......lucky get the long weekend to do!!!!






.

Bob

Hi, here I'm 7:50 in the morning to do the bob.
This unit is mostly about xolume, and who u can see the washer.
We looked volume by shell and slicing.
We learned a new way to find average value of a set of numbers.
This umit covers a lot of things that is kind of hard.
I try mu best to usr the rest of the morning to study and do good on the test.
Well, see u!!!
Hope every one do good on the tesr.
BYE!!!!!!!!!!!

Just found out that I'm the scribe for today sorry for the delay!!!
We suppose do the pre-test to day, but we are confused at certain type of question so we continued on this question:


This is the homework from Friday.

Use trapezoid sum to answer this question part a.


For part b, u basically just plot the graph out and u find it's constant at 1 to 8 so it's a straight line there the equation is -7.5r=82.5.
0 to 1 is also constant no change in slop so it's 75.
The 2ND question: draw the diagram 1st.
each one is 5 units away so it's d(0) to d(20).
then you add all of them up, it's underestimate you can tell from the graph.
I didn't really remember what we had went through in class.
Couple things to remember for this unit.
* always take a piece out of the whole solid, no there it's a disk or shell.
*dx is always means something, don't just put it in because u have to.
some helpful links to help review for the unit test:
http://www.intmath.com/Applications-integration/Applications-integrals-intro.php
http://www.mecca.org/~halfacre/MATH/appint.htm
http://education.yahoo.com/homework_help/math_help/problem_list?id=minicalcgt_6_1
hope this helps!!!!


the rest of the slides are home works to practice.
By the way next scribe is ........Kristina..............

Mar.2nd/09

It's really late now, but I will still start on my post. I might have to finish it tomorrow, forgive me for the late post.
Well we don't have the slides for today so i will write as much as i could. First thing first, welcome Mr.K back.
OK, today we reviewed last week's lesson and where we don't get or understand.( I forget my notes!!! I will do what I remember.)
1/


the 1st function is the displacement of the velocity
the2ND function is the total distance of velocity because it took the absolute value of the whole function.
the3rd function is just a positive displacement it force the negative to become positive.
Mr.K said it's not important, doesn't really mean anything.
then he made couple of example of how it works out and what are the differences.

2/the we talked about the hole which is the washer, the problem we couldn't find the washer for this one:


It came out to be 3 different question which explained why we didn't figure out.
a) is where the function y=x^2 and y=4 spinning around the axis


this graph spinning around the x-axis, it some out to be a washer and at the point (0,0) the washer ended it's filled.

b) is where the functions spinning around y=-1
we can see there is the big washer that it will never get to be filled




c) is where the functions spinning around y=4


as seeing there will never be a washer it it spinning around y=4

I have some notes that i left at school that i will edit this post tomorrow, sorry about that.
remember there is not school tomorrow afternoon
next scribe is ....................... Francis ( get the afternoon to do it!!)

Finding the arctrig derivatives

OK, first scribe for this Semester^_^
We starts off with the graph of
arc sin

arc cos

arc tan



Then we come up with the idea that arc sin and arc cos are similar, they have the same domains, they are just the inverse of each other.

Then it's time to find the derivative for arctrig:
1/ y=arc sin(x)
First let sin(y)=x sin(y)= x/1
then find the derivatives by using the chain rule

there fore the derivative of arc sin is:


2/y=arc cos(x)
well these two are the similar steps so I will use Mr. K 's work




3/ y=arc tan(x)


~something really important Mr.K talked about in class.



Every derivative rule have an anti-derivative rule:


then 2 more problem to solve:

Like Mr.K said we didn't learn a new technique to solve this type of problems. In these questions we used substitution and Integration by parts to find the anti-derivative.
Nothing much is new all we have to do is look for pattens.

Homework: ex7.5 odds and 24

next scribe is ................ Zeph

oh the chat box is there!!!
bye for now^_^

By the way Mr.K, the Chinese visitors of these 2 blogs is my friend in China that I tell her to check our blog out. ^_^ No surprising ^_^

bob

Almost for get to bob!!
well, this is a short unit, easier then other unites but also hard in some way.
I think i understand everything in 6.1 (might forget some part,but I'm try to review)
6.2 was all about accumulation function which a function in side a function. I get the idea o it, but may be not the calculation part yet. have to review that over again.
6.3 the fundamental theorem.i think i get 1/2 of it. need some more time for it too.
6.4 the area, i think I'm fine with it.
hope i can do better on this test ^_^

Jan.14th/09

Today is Paul's turn, but he is late so I'm the scribe for today.( He own me ...)


In the graph the blue area is the difference between green and orange area.
h is a tiny number that is close to 0, but not 0. Therefore x+h.
To approximate the blue area by multiply (f(x))(h).
A'(x)=f(x)
This is not a proof, but a really good augment.

We went back to yesterday's slid, the one that Mr.k made a mistake.

The statement is wrong. It suppose be
What ever you put in f(x)will end up be in f(t).

Then we worked on this problem.
1st find x^2, then us chain rule.
The inner function is x^2, outer function is f(x).
x^2 determines the limits of the integrals.

Use integrals to find the area. Accumulation function is always involve with integrals, it always requires 2 function.

t is always depend one x, always find x first.

At the end we did some questions depends on what we had learned.



OK. Next scribe is Not_Paul again. Hope you are not late again. Good luck ^_^.

The Layers of Onions

Why Onions? Well as we work through our project and complete a part of our it, it would mean that we had completed one chapter, or layer if you like, of the Onion dungeon. Here is the outlook through each chapter and sub chapters of the dungeon.

Man, I should really lay-off of those war tactics games D:

Chapter 1- IX (9): The Selection
Decide on the 6 sample questions from the textbook (questions or theme may change)

Chapter 1- XVIV (19): The Contrivance
Brainstorm and discuss about the kinds of questions should we make, using reference of the six sample question and try to make a few of them.






Chapter 2- X (10): Genesis
Create the six questions that will be used for the DEV

Chapter 2- XX (20): Decryption
Solve the 6 created question and edit the ways to solve them, making it easier to understand and cleaner to look at






Chapter 3- V (5): Initiation
We begin the making of the DEV

Chapter 3- XX (20): Sound Chronicle
We begin voice over of the DEV

Chapter 3- XXX (30): Fine Tuning
Edit what we have of the DEV






Chapter 4- VI (6): Scrutiny
Look over the DEV and discuss if it needs more work or not






Chapter 5- III (3): The Final Battle
Complete and submit the final copy of the DEV project

Chapter 5- IV (4): Epilogue
Its over!! However we have to study for the upcoming exam D:

And that is the end of our outlook of the Onion Dungeon

BOB

Well, I think I didn't do well on this unit that i need to review more. It's mostly about 1st and 2ND derivative test, i think I'm fine with that part or maybe not*_*. The Limits part was confusing, i didn't really remember much from that part. I feel like i didn't remember a thing from the optimization problems, i think i need to review more on that part. Well for the rest i still need so time to study.
Bye for now!

Dec.10th 2008

Well, in the beginning Mr.K talked about the project that is due on next Friday.
We looked at this graph again:

Mean Value theorem doesn't tells the value, but it tells where the value exists.
We went deeper to discuss what is the Mean Value Theorem.

Mean Value Theorem. Let f be a function which is differentiable on the closed interval [a, b]. Then there exists a point c in (a, b) such that




h'=f'-g' because h=f-gCorollary.

• Let f be a differentiable function which is positive on the closed interval [a, b]. Then f is increasing on [a, b].
• Let f be a differentiable function which is negative on the closed interval [a, b]. Then f is decreasing on [a, b].

The mean value theorem led us to the Rolle's theorem

Rolle's Theorem. Let f be a function which is differentiable on the closed interval [a, b]. If f(a) = f(b) then there exists a point c in (a, b) such that f '(c) = 0.


Rolle's Theorem and Mean Value Theorem is similar. but also different. Rolle's theorem starts and ends st the same spot, but Mean value theorem is not.

We did a problem about the Mean Value Theorem.

EX)



From Mr.K's work step by step.
1:use the formula to solve the slop of the secant line
2:find the derivative of the function.
3:plug the slop into the derivative function.
Therefore the answer is X=1

Home work for to night is
Exercises 5.5 # odds and 12


next scribe is Rence

^_^