In a previous pencast, I evaluate the limit of a function as it approaches a particular point. But what about evaluating the limit of a function as you move along the x-axis toward infinity? Holes exist as points on a function’s graph. Sometimes you don’t need to find out where those holes are, but you want to find out what the y-coordinate of a function moves towards as x gets really big. Remember — infinity is an idea, not a number; just like dividing by zero doesn’t leave you with a number for the answer.
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The visual component behind how to find a horizontal asymptote at y=0 was a good tool to memorize, but I personally don't like to use any tool unless I know at least in general where it came from. Just from basic knowledge of horizontal asymptotes, it is a value of y that cannot be used. Generally, when the asymptotal value is substituted in, the x's in the equation cancel out and is left with an untrue statement of constants, proving the asymptote is there. But with an asymptote of zero, that direct approach wouldn't exactly work.
This was a good video in understanding when a limit of a function approaches zero when x goes to infinity. I think it would be a good idea to include when the degree of the polynomial is equal on the numerator and the denominator. It is easy to understand from this video that a function will approach zero when x goes to infinity if the degree of the polynomial is greater on the bottom than the top. That is basically the only concept I got out of this video. I think it would be a good idea to include another example different than the one explained. This is good to develop a basic understanding, but I think that more information could be included to go further with this topic.
I liked this pencast. It made sense to me and it went through the x and y asymptotes. It also helped me understand how to find limits as x approaches infinity. I like how it went step by step and was easy to understand. I like how it tired the asymptotes into it as well.