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.
So, have you read the blog-online rules? Have you watched the video? Have you finished your homework? If you haven’t done so, please do.

Talking about unlimited amount of math, Mr. K introduced a very interesting approach to


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!


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

What if x = 1?

  • 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 !

1 comment:

  1. Hi Vincent,

    An outstanding scribe post; I'd say you've enhanced everyone's learning with your clear explanations and illustrations! In addition, the "title" graphic and encouragement to others to develop self responsibility are excellent!

    Very nicely done!