Thursday, February 28, 2008
Tuesday, February 26, 2008
Wednesday, February 20, 2008
Limits
Why hello there!
Kristin here - reporting the events that took place in todays' Calculus class.
The day started off with introductions to Mr.Rekrut- our substitute teacher for the class, with his first words being, "Looks like you have a quiz today" ....a little shocked, not going to lie.
Luckily, it was only four questions involving the simplifying of problems with exponents, factoring with exponents, finding the equation of a line in general form given the slope and a point on the line, and finding the equation of a line given a point and a parallel line.
Then we were assigned pages 45-58 in the orange and white booklet, as well as pages 6-8 in the blue booklet, which I'm assuming are due for next class, seeing as how we don't have one until next week..
If there is anything I forgot, please let me know....
The Scribe for next class is....SAMUS!!!
Kristin here - reporting the events that took place in todays' Calculus class.
The day started off with introductions to Mr.Rekrut- our substitute teacher for the class, with his first words being, "Looks like you have a quiz today" ....a little shocked, not going to lie.
Luckily, it was only four questions involving the simplifying of problems with exponents, factoring with exponents, finding the equation of a line in general form given the slope and a point on the line, and finding the equation of a line given a point and a parallel line.
Then we were assigned pages 45-58 in the orange and white booklet, as well as pages 6-8 in the blue booklet, which I'm assuming are due for next class, seeing as how we don't have one until next week..
If there is anything I forgot, please let me know....
The Scribe for next class is....SAMUS!!!
Monday, February 18, 2008
Whoa! I can’t remember the last time I blogged for Math! But, yes, again, blogging is a very important instrument to enhance knowledge and develop self responsibility (remember the escalator video..). It is our utmost responsibility to do things ourselves even though we tend to lean on others – which means:
- do our homework
- try to blog as extensive as possible for it determines how well you know the material
- read scribe post everyday
- ask questions if necessary
- always check for misinterpretation by peers so that no one else will be confused and eventually mess up a test or exam in the future.
Talking about unlimited amount of math, Mr. K introduced a very interesting approach to
UNIT 1: LIMITS
What is a limit? The first time I heard it was when I watched “Mean Girls” back then. I didn’t know what it was. Yes, 5 years after… here it comes, slowly making sense. Yes, AP CALC people, you can laugh since we’re only at the threshold of the house you have already explored three times! Here it goes.
This notation is used to express LIMITS, which means if you do not have this in every line, the entire thing is incorrect!
PROBLEM #1:
What do we first notice about this equation?
- a second degree function (x^2 : parabola) over a first degree (linear)
- a difference of square in the numerator
- if we graph this on our graphing calculator, it’s a straight line, opposing the fact that it should be some kind of a parabola. Hmmm, weird.
What happens if we factor the numerator?
- the (x-1) reduce
- we’re left with f(x) = x + 1
- graphically, it is identical to the graph we had earlier when we graphed the original equation
- Most of the students would say, “IT’S 2!” because of the equation: f(1) = 1 + 1 = 2
- However, some might disagree and say, “It’s undefined, buddy!”
The question now is WHY? Well, f(x) = x + 1 isn’t the original equation.Therefore, substituting 1 for all x gives us:
This brought the discussion about the very round number called ZERO. Usually when we divide any number by zero, we say “YOU CAN’T!!!”. It’s very hard to explain. Actually it’s pretty simple. You can’t divide by NOTHING! This follows the same curvature of the ball of wax. Anything over ZERO is undefined… it’s not two… again, it’s undefined!
We also had a discussion about 0/0 is not 1, why is it so different from 2/2 = 1?, when both 0 and 2 are numbers? Isn’t a number divided by itself equal to 1? Why is zero such an exception? Well it could mean NOTHING, INFINITY, or ZERO. It all depends on the hwo you look at it. Interesting… Mr. K, took out his “block of wood” to further discuss how you can look at something at different ways but it still refers to the same thing.
Consider SLOPE. It can be represented in three ways:
- m
- y = rise / run
- y = delta y / delta x
So, why do we have three ways to describe slope? ANSWER: because we have three ways to illustrate a function:
- equation – where ‘m’ is present in the standard form of a line (y = mx +b)
- numerically (table of values) – where we can take two ordered pairs and put them into the equation
- graphically – where we can locate two a point and use y = to find the slope.
In this case, f(1) is in an indeterminate form, which means, when x = 1, it is undefined. To prove this, we can graph the equation one more time. But this time, hit ZOOM 4, which will provide you with a much closer scrutiny at the graph.
Look at the gap on the linear equation. Isn’t it weird? Well that’s exactly what we had earlier. f(1) ix not 2. Because the point missing on the graph. Try tracing any integer greater or less than 1. It will give you the y-value but will not do it so if you enter x = 1. This squeezes out the value of 2 from both sides - >2 and <2.>
Let's take a look at a very similar problem:
As the end of class approaches its LIMIT, Mr. K, very quickly went through the laws of limits with all the mathematical operations (addition, subtraction, multiplication, and division). They are on the slides posted of Friday! It's pretty simple. It's somehow like logarithms but not really! AND AGAIN, MAKE SURE TO INCLUDE THE PROPER NOTATION FOR LIMITS OR YOUR WORK WILL LOSE A VERY FRUSTRATING AMOUNT OF MARKS!
We had a glimpse of the graphs of limits at the end of the period but since I was not sure about how it goes, I chose not to include it here. I hope Mr. K further go into details about that one in class next next class (he won't be here on Wednesday, which is the only class we have this week). This concludes my scribe post and I hope everyone had a great 3-day weekend! If you didn't, don't worry, there IS another one! YES! Anyway the next scribe will be...
K r i s t i n !
Friday, February 15, 2008
The Scribe List
This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.
This post can be quickly accessed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.
Cycle 1
This post can be quickly accessed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.
IMPORTANT: Make sure you label all your Scribe Posts properly or they will not be counted.
Cycle 1
haiyan MrSiwWy | Grey-M John D. | rusz.l |
Thursday, February 14, 2008
February 13 / 08 - Scribe
I will be taken Vincent's scribe duties as he requested.
Mr. K was not present in class today so we had a sub. This class was a working period to do the review booklets. (Blue, White/Orange)
The new assignments are: Read pages 30-45 (White/Orange book), Do page 5 (blue book).
That concluded the class of February 13!
The next scribe will be: Vincentr!
Mr. K was not present in class today so we had a sub. This class was a working period to do the review booklets. (Blue, White/Orange)
The new assignments are: Read pages 30-45 (White/Orange book), Do page 5 (blue book).
That concluded the class of February 13!
The next scribe will be: Vincentr!
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