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Friday, December 12, 2008
"Mr.Kuropatwa"-less
Funny thing is that I didn't even realize that I was scribe until I went to check the blog before heading off to bed.
And what do you know, I'm scribe. Oh what joy.
Anyways, we had a substitute today. Her name was Mrs. Mandag I do believe. Initially, she told us a little background information on herself, and her involvement in the Winnipeg School division, having previously taught at St.Johns High School and Sisler High School. She also mentioned her contribution to the Math curriculum of Manitoba. I can't remember if she said it was for grade 10 or grade 9.
Anyway, we were assigned the even numbered questions of # 5.5 for class.
Next scribe will be benofschool?
And what do you know, I'm scribe. Oh what joy.
Anyways, we had a substitute today. Her name was Mrs. Mandag I do believe. Initially, she told us a little background information on herself, and her involvement in the Winnipeg School division, having previously taught at St.Johns High School and Sisler High School. She also mentioned her contribution to the Math curriculum of Manitoba. I can't remember if she said it was for grade 10 or grade 9.
Anyway, we were assigned the even numbered questions of # 5.5 for class.
Next scribe will be benofschool?
Wednesday, December 10, 2008
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-g
Corollary.
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.
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-g
Corollary. - 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
^_^
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
^_^
Tuesday, December 9, 2008
The "Mean" Value Theorem
Willy the Wallaby is back and this time he is not looking for a job! This time he needs to build a cage fo0r his new pet Bob, a boa constrictor. The volume of the cage has to be 4000 ft3 and the length is 5 x the height of the cage. That is not all Wally has to pay with his own money, probably from his new job, to build the cage. So Wally wants to build the least expensive cage that has the correct volume, length and height. For the materials it cost $ .25/sq ft
Even though I worded it differently it still has the information for what you need.
1) What are the dimensions of the least expensive cage?
And Mr. benofschool was kindly enough to show us how it was done. To start things off first list down the information that is given to you
height = h
length = 5h
volume = 4000 ft3
width = w
Seeing that the width and height are unknown and that the length is determined by the height, we find the width first.
Then we find the surface area of the cage, which is needed to solve for the total amount it will cost Wally to build it.
At this point you find the derivative of the equation
Next you let "h" go to zero to find what "h" is at that point.
and prove that "h" is what it is by using the first derivative test
and finally using the new found height you can now solve for the rest of the dimensions of the cage.
2)How much does it cost?
For this question there is nothing special about it just fill in the numbers \:
After taking most of the class time to solve the one question we move on to the beginning of the "mean" value
In this graph the first red line (i)is called a secant line, which is the mean, or the average of the line f(x).
If this was a graph of a person's change in velocity while driving, he would have his license suspended, but since this is in a Calculus class we don't even care if that person was fined or not. In the changing velocity graph the secant line is the person's average driving velocity, and the only once that the person drove at his/her said average, which is where the secant line cross the f(x) line.
Plus another thing about this graph is that at point c (both of them) the slope at those points are the same as the slope of the secant line, but to find the slope of a secant line, you need to use this formula:
Finally the next scriber will be Yinan,
*rants*
and because a certain someone had me to scribe today I had to cut my hours short from volunteering at the hospital helping the community and making people happy to get to feel better in this crummy weather!!! Which had added a lot of work on me for today!! And now I will have to stay up late to make up for my lost hours typing this post!! And as for Mr. Racoon this is what he thinks of you when you get me post on a Tuesday night.
Even though I worded it differently it still has the information for what you need.
1) What are the dimensions of the least expensive cage?
And Mr. benofschool was kindly enough to show us how it was done. To start things off first list down the information that is given to you
height = h
length = 5h
volume = 4000 ft3
width = w
Seeing that the width and height are unknown and that the length is determined by the height, we find the width first.
Then we find the surface area of the cage, which is needed to solve for the total amount it will cost Wally to build it.At this point you find the derivative of the equationNext you let "h" go to zero to find what "h" is at that point.and prove that "h" is what it is by using the first derivative testand finally using the new found height you can now solve for the rest of the dimensions of the cage.
2)How much does it cost?
For this question there is nothing special about it just fill in the numbers \:
After taking most of the class time to solve the one question we move on to the beginning of the "mean" value
In this graph the first red line (i)is called a secant line, which is the mean, or the average of the line f(x).If this was a graph of a person's change in velocity while driving, he would have his license suspended, but since this is in a Calculus class we don't even care if that person was fined or not. In the changing velocity graph the secant line is the person's average driving velocity, and the only once that the person drove at his/her said average, which is where the secant line cross the f(x) line.
Plus another thing about this graph is that at point c (both of them) the slope at those points are the same as the slope of the secant line, but to find the slope of a secant line, you need to use this formula:
Finally the next scriber will be Yinan,
*rants*
and because a certain someone had me to scribe today I had to cut my hours short from volunteering at the hospital helping the community and making people happy to get to feel better in this crummy weather!!! Which had added a lot of work on me for today!! And now I will have to stay up late to make up for my lost hours typing this post!! And as for Mr. Racoon this is what he thinks of you when you get me post on a Tuesday night.
Monday, December 8, 2008
The Scribe List Version 12.5
Cycle 12
Quote of the Cycle ;
"I've missed more than 9000 shots in my career. I've lost almost 300 games.
- Michael Jordan
Rence ~ Out
zeph yíＮＡЙ | Not Paul |
|
"I've missed more than 9000 shots in my career. I've lost almost 300 games.
26 times, I've been trusted to take the game winning shot and missed.
I've failed over and over and over again in my life and that is why I succeed."
- Michael Jordan
Rence ~ Out
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