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Wednesday, December 3, 2008

Inifinite Limits

Today in class we spent the majority of our time learning, and expanding our understanding of infinite limits and asymptotes, of both the horizontal and vertical type. First off, I'd suggest you watch the video found on the slides of today's slide show, because it's very informative and useful when it comes to better understanding this unit, which will help you understand this scribe post (hopefully). We started out about stating how infinite limits come in 2 "flavours" when a limit of "x" goes to some value, and that equals infinity, or approaches infinity, since infinity isn't a number. The other "flavour" is when the value of x approaches infinity and equals to some value. Those are the 2 main rules.

We also mentioned sequences and series. Where sequences are a series of numbers, that follow some rule, and are related to each other by this rule, and a series is the sum of the numbers in a given sequence. I'm not entirely sure why we mentioned this, but I think we brought it up to further understand the value of infinity, or the not-value of infinity, since infinity isn't a value at all, if that makes sense.

Okay so found in slide 2 of the slide show from today's class, we can see the equation that looks something like this : f(x) = (x-a)(x-b)/(x-c)(x-d), this is pretty much the general equation we used for the whole class. With this equation, we looked at how to find asymptotes, of the horizontal and vertical type. A little note about asymptotes: the graph doesn't necessarily leave these sections "untouched" it depends on what section of the graphed function you're looking at, because there can be a section of the graph, that might actually touch or cross where the graph isn't shown.

In a rational function when the denominator equals 0, we have a vertical asymptote. With this said, the denominator determines the vertical asymptotes, and the numerator determines the roots of the graph. Vertical asymptotes are related to limits when x approaches some value and the result is infinity, and horizontal asymptotes are related to limits when x approaches infinity and the result is some value.

Horizontal asymptotes are found on slide 6 of today's slide show. To find the asymptotes we lower the our highest given degree of a polynomial to 0 (the power on x). We multiply the numerator and denominator by the reciprocal of the given polynomial, as found in slide 6. After doing this, we should be left with the coefficients of those polynomials we reduced. All the other values should be over "x". When infinity is substituted into these x-values, then those values won't exist, and your just left with the coefficients, which will be your horizontal asymptote.

Doing these steps are important because if you substitute infinity into the x-values of the original equation, then most likely the result will be infinity divided by infinity, which does not equal 1! This is called an indeterminate form, other indeterminate forms are 0/infinity, infinity/o and o/o, in university if you decide to take calculus, you will further learn about these indeterminate forms. If you get a indeterminate value of 2/0, when trying to find the horizontal asymptote, then there is no horizontal asymptote, but instead might be a slanted asymptote. Also, if trying to find the horizontal asymptote, and the value is 0/1 then the horizontal asymptote will be the x-axis, regardless.

That pretty much sums up our class. All fun stuff aside. Hopefully you guys watched that video like 20 times like me.The homework was exercise 5.3, all the odd questions including 6 and 20. The next scribe will be Kristina, because I guess she's first on the list.

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