BOB

Hi! I like differentiation rules because they're straightforward. If two terms are multipled together, we use the product rule. If they're divided, we use the quotient rule. The reason why I think we're anxious about antidifferentiation rules is because there are no guarantees that we're even on the right track. There are guidelines that we've discussed over and over again, but as we all know, sometimes we still end up being on the wrong road. As with everyone in the class, I don't feel the best about this unit either. I DO believe though that we'll get through this, and we'll turn out alright. Remember that we took this class, among other things, to get exposed with the material? to be prepared for university? Well, I say let's work our butts out right now too, cause if we don't, we're just wasting our time.

BOB

I am not even going to lie and say I understand even the simplest part of calculus . . . it's some hard stuff. I really don't understand much of the material. I just get confused with anti derivative and derivative and the chain rule, integration by parts. There's too much going on in one problem. My brain's exhausted just from thinking about The composite of functions and the product of functions. I really wish I understood calculus but I don't think that math is one of my strengths as some people are good at some things other people are not. I'm just trying to hang on to this class and hopefully come out of it with some knowledge and hopefully it will help me later on in life and if it doesn't at least I can say I tried. So what am mostly confused about is the general stuff like how to use integration by parts otherwise I really don't know.
I am going to go and try to attempt the chapter 7 review one more time and hopefully I'll get some of my confusion cleared up.

Scribe

What did we do today?

We discussed how the pre-test went with the substitute and the multiple choice questions were pretty straight forward and no one really had any problems. What did leave us all puzzled was the long question in the back, the "open response".


The question was . . .

(1) Let f be a differentiable function such that f " is continuous and f and f ' have the values given in the table below.

(now I wished I had the smart board so I could draw the box like Mr. K had done in class..ah the wonders of technology, I honestly can't keep up with it.)




Don't forget the mnemonic " LIATE ".

L ogarithmic
I nverse trignometric
A lgebraic
T rignometric
E xponential

So an example problem that we did that even got Mr. K, who's a math gyro (uh I don't know if I am using that word right) thinking was . . .



So to review . . .

+ When the integral is a composite of functions, you are better off using substitution.
+ when the integral is a product of functions, you are better off using integration by parts.


Last but not least next scribe is Suzanne.

BOB

Everything was quite clear when we started this chapter. That is, until we got to 7.6 everything I thought I knew completely left me. I'm not sure if I'm ready for this test. The pre-test was going great until the open response question. My confidence just left me. For the next couple of days, I'll have to do some MAJOR reviewing.

Ants? Geese? Calculus?

Concerned after reading your BOB's and wondering if you've forgotten these:

The excitement of an early Hall of Fame scribe

How much you supported each other

Linger’s "Won’t let you Fall"

"Lessons from the Geese"

Yes, it's second semester. Yes, the schedule is hard. And yes, there's so much to do--

Didn't you have something pretty special? Is it lost? Can it be found?

Today's Slides: February 27

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

bob

all i can say is that this unit is very hard. it made it more difficult because we only had class every other day so it was hard to remember all the things that was going on. also it was hard to do all the homework since there was alot of other homework from other classes. but i know that it is all my fault lol, i cannot blame anyone. next time i will be sure to do all my homework. p.s. i don't think i am ready for this test lol

bob

all i can say is that this unit is very hard. it made it more difficult because we only had class every other day so it was hard to remember all the things that was going on. also it was hard to do all the homework since there was alot of other homework from other classes. but i know that it is all my fault lol, i cannot blame anyone. next time i will be sure to do all my homework. p.s. i don't think i am ready for this test lol

BOB #7

Well, everyone else more or less summed up my situation. I felt that I had a fairly good grasp of the stuff we covered at the beginning of this unit when last semester came to an end. And this semester, what with only having class every second day and missing a number of classes due to tours, illness, etc. I have forgotten what I knew. I think if I had done the test back when we were on exercise 7.5, I would have a better chance than doing it now. It's just that too much time has passed, it's like coming back from summer vacation... The pre-test was difficult for me, I used my calculator for all the multiple choice so I think they're right, but though I had several ideas for answering the long answer, I don't have much confidence in what we finally decided to hand in. Having class every second day makes me procrastinate more than usual. But however this unit goes, I am going to get back to my usual (relatively) good habits for the next unit. I promise!

BOB

I am honestly disappointed in myself. I know I could do so much better. But it's all my fault that I've done so bad in this unit. I barely attempted my homework... and I feel so awful ( that's currently changing) I know I'm going to do bad in my test. I think I'm in some sort of denial. I say I want to do a good job, but then why do I keep digging this hole for myself that I can bury myself with later. If I really really wanted to do a good job then why am I not doing a good job. It's weird for me. I have that turning feeling in my gut. That's guilt. I haven't felt like this before about a class. I usually do much better. I think I've just really hit my turning point. I am, FOR SURE!!!, going to do my homework. I'm making my mom check my homework from now on! It's kind of sad that it had to come to that, but if it's what I have to do to get better than it'll be worth it. I think it's kinda late for that but at least I'm going to keep trying. We still have like 2 units left or something. Like everyone else is saying, having calculus every second day is bad! I think that it's good for me to be brutally honest because it's helps me accept that I'm not doing the best that I could and I want to change that, honestly.

Blogon the Blog #7

Ooo, I almost forgot to blog! Like others I'm having difficulties with this unit. Friday's pre-test seemed fairly easy for the first part... well the multiple choice anyway. But everything was pretty much solved using a calculator, which probably isn't a good thing in the end. For the long answer part, I was a bit sketchy about. Although I'm pretty sure we'd use integration by parts to solve for the definite intergral, but still remain second guessing myself. I think I'm pretty good with my arc functions and finding the intergral that involves the usuage of them. If there is any problem solving questions available, I think doing those will sure help us understand more. And I agree with others that having calculus class every second day is different... but we just have to adjust. It's a bit troubling for me because some of us have physics every other day we dont have calculus, but I'm taking it for the first time. But, in the end there should be no excuses. I really just start to get cracka-lakin down to business!

BOB

Wow, this chapter was and still is really difficult. During the class discussions and Mr. Kuropatwa's explaining I have a good grasp on the work and what's going on. However when I get home and attempt some of the questions on the assigned exercise it takes me a really long time to solve it, if I even succeed in finding the right answer. It's like the light burned out or something. I again have a lot of reviewing to do. Those antiderivitives just do not want to be found. Well I guess I'll have to read some of the text and my notes to do well on this test. A review next class would be helpful though :) I'll probably try some more of those supplementary problems. Good luck to everyone and study hard.

BOB #7

This chapter on different ways of finding antiderivatives is truly a chapter that I found quite difficult. I think its the amount of methods that I got confused with. I wasn't sure whether to use the substitution method or the integration by parts method. I still understand how to use the substitution method but when I went to look back at my notes, I totally forgot how to use the integrartion by parts method. I agree with people in the class who believe that having class each odd day is a disadvantage. It's a disadvantage because for me, I end up forgetting most of the things I've learned in class. I guess that's why I do need to study each day so that when the next class comes I don't forget any lessons that I've learned from the previous class. My goal for the next chapters is to do the homework right when it is assigned and to study the lessons each day instead of leaving it to the end. Test is tomorrow and I have to admit that I'm not fully ready. Right now I feel like I really really need to study. I hope everyone studies too and does well. good-luck =)

BOB

Hi everyone! We have finished Chapter 7 and we are now getting ready for a test. For me, this unit was very hard. Finding the antiderivative is harder than getting the derivative because there are no rules to find an antiderivative. From what I observed, Mr. K explains everything well. When it comes to doing the homework exercises, it's very hard to answer. I guess we just need more practice. I'm scared for the test because Mr. K gave us a pre-test without him. I hope we go over the answers before having the test. But for tonight, I need to go over some stuff and make sure I know how to solve antiderivatives. Good luck everyone!

BOB

Hey hey hey... another unit down, another BOB to put up. I must say, having calculus every other day is no fun at all. I feel like there's more pressure to do the homework and to be honest, I still haven't done it all. I don't know what it is... maybe it's what Mr. K is saying, how we're tired and we don't care as much. I mean I want to do good in this class, I'm just getting super lazy. I was lost with the open response question on the pre-test. I dont think this unit was super duper difficult. I just think that I haven't been giving it a hundred and ten percent. I pay attention in class and I understand... but since we only see each other every other day and sometimes longer, the thought leaves me after I walk out of class.. and I've been putting off the homework because of all the other classes and other activities going on. I still need to review my notes and finish my homework to prepare for the test. Having calculus every other day scares me, because everything is happening so quickly. It's almost March... which reminds me, aren't we suppose to be writing that exam this month?!? Mr. K?!? Our Panda Project is far from being done, and my group still hasn't started on our video project.. I don't think anyone has. There's just always something going on. I haven't had a free lunch period in a long long time. Even with my spares, I feel like I'm running out of time. Ohhh, it's all about this semester. There's only two more units left. We're so close guys... and I want to get it over with but then again I don't. Can we please have a review day next class?!? I feel like I'm not ready for the test... && Good luck guys =)

Well this class was pretty funny we were all really lost and confused with the pre test open answer question. Instead of forming three people groups like we usually do, we formed one big class group and tried to help each other out.

Chapter 7 pre-Test: Antidiffernetiation

Multiple Choice
The multiple choice were pretty much calculator work. I will just list the answers our group got.

#1) If the definite integral 1S3 (x²-1)dx is approximately using the Midpoint Rule with n=4, the error is:
(B) 1/24
#2) If -1Sk (3x²-2x)dx=6, then k=?
(D) 2

#3) If 0Sk (sec²x)/(1+tanx)dx=ln2, and k>0, then the value of k is:
(B) 3.14/4

#4) Let R be the region in the first quadrant enclosed by the graph of y=xcosx, x=0, y=0, and x=k for 0<(3.14/2). The area of R, in terms of k is:
(A) ksink+cosk-1

Open Response
This is where all of us (as a class) just became clueless. We looked at it for a long time and read it over again, but we were not 100% or even 90% sure what to do or where to even begin. We're not sure what that -2 is all about and if it's supposed to be in that missing spot in the table.



#1) Let f be a differentiable function such that f " is continous and f and f ' have the values given in the table below.

Use the information in the table to evaluate:
a) 0S2 xf ' (x²)dx
15.333...

b)1S3 xf ' (x)dx

This was the answer our group got (aka manny figured it out :) ).

Well that's it for that class. As a class we are really confused about this section, we feel we're not ready for that test on tuesday. We just need a huge review Mr K., a HUGE review.

Oh the scribe for next class is ANH :)

BOB

Well, i know it's early , but im not going to delay this. It has been tough these last two weeks back
, since we only have class like every second day. =T tomorrow we have a Jr High tour, so that means our test might be on Friday? or Next Tuesday? I'll admit i am finding it difficult to even review and practice for unit seven. The test dates keep moving farther away and i do my other subjects first. I am going to try my best to get some study time down for this unit. Everything is confusing... good luck everybody =).

scribe post

hey everyone as you all can see its charlene here and yes i am scribe for today. today we started off with a quiz just like every single class from now on. so the quis consisted of four questions and we got like eight minutes to do it. we did go over some of the questions on the quiz so here they are...

A) given f(3)=8 and f'(3)=4 find f(3.02)

y - y1 = m ( x - x1)
y - 8 = -4 (x - 3)
y = -4x + 20

y(3.02) = -4 ( 3.02) + 20
Y(3.02) = -12.08 + 20
Y(3.02) = 7.92

B) given y=1 and xy² - 2y 3 4y³ = 6

solve for x
x - 2 + 4 = 6
x = 4

differentiate
y² + 2xyy' - 2y' + 12y²y' = 0
y' ( 2xy -2 + 12y² ) + -y²
y' = -y^{2<.sup> / ( 2xy - 2 + 12y2}

y'(1 , 4) = -1 / 18

after reviewing some of the questions on the quiz mr.k gave us a table to fill out that consisted of the trapazoid sum, reiman sum, and the simpson sum

i wasn't allowed to upload the table so im just gonna type it on

N ..Tn ....... error ..... Mn ....... error ..... Sn .....error
4 ...0.2656. 0.0156 ... 0.2422 ..-0.0078 .. 0.25 .. 0
8 .. 0.2539 .0.0039 ....0.2480 ..-0.0200 ...0.25 ...0
16 .0.2510 .0.0010 ....0.2495 ..-0.0005... 0.25 ...0

Tn = (B + B)H / 2

Mn = REIMANN SUM
*use 0.5 as the x-choice

Sn = T + 2M / 3
* WE DO NOT HAVE TO KNOW THE SIMPSON SUM FOR ANY TESTS OR EXAM

ERROR = approximation - actual

unforntunately i do not understand the table as much as i should so i will just wait till monday to explain more clearly what is going on in the table. sry guys

by the way the next scribe is CRYSTAL

Scribe Post: Day 82

It's Danny! The day started off with a multiple choice quiz which we will be having every class in preparation for the final exam.

After that Mr. K gave us three integrals to antidifferentiate. When solving these three questions you must consider these two derivative rules:

Now onto the questions and solutions:

QUESTIONS:


SOLUTIONS:




After that Mr. K talked about "Trapezoid Sums" and "Midpoint Sums". I'll sum it all up in four simple diagrams.

For Trapezoid Sums when the curve is concave down, the sum would be an under estimate. When the curve is concave up, the sum would be an over estimate.


For Midpoint Sums, if you rotate it and make it a line tangent to the curve you'll see that when the curve is concave down, the sum would be an over estimate. When the curve is concave up, the sum would be an under estimate.

Well that's all I was able to muster up for this class, as you all know Charlene was the next scribe, her post is already up. Enjoy!

I also have a very important announcement to make. Even though I was convinced to stay in the course by Mr. K himself I truly believe now that it's best if I don't continue on. I experienced something in our last class that couldn't be a better reason for my leaving. I was having trouble with completing a chart, not only because I was unaware of the fact I was doing my task improperly, but also because there was something in there that I SHOULD'VE KNOWN from past pre-calculus courses that I completely forgotten. That explains to me that I haven't done my past math courses to the best of my ability, therefore hindering my learning experiences in my present math courses. I've already begun trying to fix up my past by taking my PRECAL 40S course again. This decision hopefully will allow me to take Calculus again in University, and this time understand things completely with the mind set of thinking I know material I should know and that'll make things easy for me. One last thing, I know Mr. K you tried to keep me in your class and you succeed. However, this time I've decided and no matter how disappointed you may be, I feel this is the right thing for me to do in my life and my soon to be career in education. Please I'm not asking you to agree with me on my decision, but I'd like to know you're always there for me when I need you. I'm terribly sorry Mr. K, but I'm not going to ask for your forgiveness on my decision.

Scribe Post: 81

Hello everyone! Today, Mr. K talked about Gr.9's from other schools who are going to take a tour of Daniel Mac and how we're going to be teaching them how to do several games. We decided on 5 games but one of the games is yet to be changed.

Here is the draft of whose in what group and whose in what game:

1)Game: Magic
Group:
-Jann
-Mark (a maybe)

2)Game: River
Group:
-Lindsay
-Danny
-Christian

3)Game: Hanoi
Group:
-Suzanne
-Manny
-Katrin

4)Game: Painted Faces **Has yet to be decided on**
Group:
-Linger
-Danny
-Mark

5)Game: Tangrams
Group:
-Charlene
-Anh
-Ashlynn

At the end of Class Mr. K talked about the rules of the Calculus Exam.

**keep in mind that nobody is NOT allowed to say a word about the exam EVER
**remember in the exam it's better to skip and not answer a multiple choice question than to just totally guess on a multiple choice question. ***you will NOT lose any marks if you skip a multiple choice question***...but if you totaly guess on a m.c.q. and you get it wrong, marks WILL be deducted.***

NOTE:
-starting next class we will be doing timed multiple choice quizes at the beginning of class to prepare us for the exam! DO NOT BE LATE FOR CLASS b/c we're going to be timed!

Homework: read the next exercise: 7.6 (it will help you for the next class)

NEXT SCRIBE: DANNY (for friday's class)

Scribe Post

Hey everyone! I tried making my scribe as a stop-action animation but I couldn't get it to work right so I guess I'll make it the old way...





With this definite integral, we can find its antiderivative and find the area.














Let's take a look at the graph...




Solving problems like this are not always this easy as this one. We can't always find the exact value of the definite integral.









Take a look at this problem and its graph.












We could use Riemann sums to find the area under the curve.

















____________________________________________________________________

These are the differentiation and integration formulas. We use these to help us determine the problems below.

















Determine:

1)
Use substitution. (I FORGOT TO PUT dx INTO THE PICTURE)
u= x ³
du= 3x²
1/3du= x² dx



If your wondering why u = x³ its because

(x³)² = x⁶. So u is u². We are trying to make the original function look like d/dx Arctan(x) integration formula.

Substitute ....................................................Resubstitute








You don't need " + C " in the intermediate steps because the C are not the same while your substituting.



(There's supposed to be an equal (=) sign in between the pictures)
_____________________________________________________________

2)
If the 8 was a 9 in the polynomial we could complete the square.
So we do this,
6x-x² -8 Factor out the negative.
-[(x² -6x+8 +1) -1]
-[(x² -6x+9) -1]
-[(x-3)² -1]
1 - (x-3)² We can replace this into the integral.

Next we use substitution.

Let u = x+3

du = dx






Then RE-substitute..






And we're done




Homework: finish up arctrig exercises (7.5)



Wednesday's scribe will be Katrin.

Scribe Post

THIS IS LINDSAY! On the last day of semester 1's Calculus class, which was Thursday for those who do not remember, Mr. K had to supervise the Pre-Cal Provincial Exam, so we were on our own! We were given two worksheets to do and we worked on it as a group. We only finished one problem though, but that's okay. TEAMWORK!!




Wrong Way Joe!



Joe Physics was driving down the highway on this past Memorial Day weekend. Joe's car ride was getting boring so he decided to calculate his total distance from his house from t=1 to t=3. Normally he could have used his odometer, but he drove backwards on part of the trip. Joe figured that his velocity as a function of time could be given by v(t)=3t^4cos(t). If at t=1 his displacement is 5 what is the total distance traveled by Joe from t=1 to t=3 using integration by parts?





This is what we came up with as a class. XD

















On Friday we went to the University of Manitoba for a workshop on "Personal Learning Environments: A Better Learning Landscape?" It was quite fun. =) Driving down the highway with the Calculus class. I thought it was a day well spent. Bravo to Mr.K for his awesome improvisational skills.

The related rates photo is due on, I believe, Tuesday.

I hope everyone did well on their exams. BACK TO CLASS TOMORROW! Next scribe is ASHLYNN!