BOBBING FOR MATH

What can I say about this unit? We'll it was the first unit for Intro to Calculus and it was really boring and like bland. It was hard not to get distracted by other things. Limits isn't hard it was just writing everything out that I would forget to. Sometimes I wouldn't see the dots and thats where I lose marks. Other than the boring mechanical stuff limits was okay. That was a fast unit. We'll I guess I'm happy limits is over with.

MORE LIMITS

THURSDAY'S CLASS

We started off class with a quiz. It had two graphs and we had to find the limit of this and that. We marked them in class and went over some of them. We mainly focused on the different type of graphs that are discontinuity. The three different types of discontinuity are:


1. Removable Discontinuity:
A hole in a graph. That is, a discontinuity that can be "repaired" by filling in a single point. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.



2. Jump Discontinuity:
Jump discontinuities occur where the graph has a break in it is as this graph does. It can't be fixed or repaired so that the graph is continuous.





3. Infinite Discontinuity:
A discontinuity of a function for which the absolute value of the function can have arbitrarily large values arbitrarily close to the discontinuity. Can't be fixed either.

The formal way of telling what kind of discontinuity it is:


Then we worked on some questions in class.


We also did some work on Mr. K's favorite website for limits ( i think ). We worked together as a class to solve them and they're all on the slides that Mr. K posted up on the 28Th. It also has explanations and the homework assignments. And that was Thursday's class.
The next scribe is KIM POSSIBLE. Ha ha i totally ripped that off from your brother but he's not around.

L-I-M-I-T-S

TUESDAY'S MATH CLASS

Someone forgot to scribe for Tuesday's math class and she's making up for it by scribing for Tuesday and Thursday. Sorry. Well, on Tuesday we mainly focused on limits in a symbolic approach. The first question was....

1. Factor both the numerator and denominator. If you don't factor the numerator and denominator and go straight to substituting in the value 2 for x, you'll end up with zero in the denominator making the whole thing undefined.
   
2. Reduce
   
3. After reducing the same terms in the numerator and denominator you substitute the value two in everywhere there is an x.
   
4. Voila, you end up with the answer.

1. Rationalize the numerator because if you do then you can reduce 25 - x in the numerator and denominator.
2. After reducing, you're left with 1 over 5 + √x. You can now substitute the value 25 for x because it's in its most reduced form.
   
3. Now simplify, the √25 is 5. What is left is 1 over 10.
   




The whole thing is undefined because in the end your gonna have to substitute zero in for x and 3 over 0 is undefined. Any number over zero is undefined.




1. The numerator can be factored so that something can be reduced from the bottom.
2. After reducing to the simplest form you now can substitute the value nine for where there's an x.
   
3. The end result is negative 6.





That would have been marked wrong if it was on a test or exam. Why?
Well, in the end since it's just the notation and you've solved for it, you don't need the lim thing.


For the rest of the class, we briefly talked about horizontal and vertical asymptotes. Homework was posted in the slides.