WEBVTT
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all right, we want to find a limit of
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this expression as X approaches positive infinity. Since X
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is going to be approaching positive infinity, it's going
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to be positive and it's going to be very large
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and then larger and even larger. So when we
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look at the numerator, X to the fourth minus
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three X squared plus x. Even though we have
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three terms uh as X gets very very large uh
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one of these terms, the one with the highest
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power is going to be the dominant term, so
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the numerator is going to be dominated by extra fourth
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uh because as X is very large, exit 1/4
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will be extremely large three times X to the second
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won't be anywhere near uh you know, as large
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as X to the fourth. So even though we're
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subtracting three X squared uh this whole numerator really is
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going to be dominated by the highest power backs D
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x to the fourth term. Likewise, the denominator
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is going to be not is going to be dominated
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by the X to the third term. So this
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entire expression is basically going to be dominated by X
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to the 4th over X to the third as X
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approaches positive infinity Now exit the 4th divided by extra
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3rd is really x. Okay, so as X
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approaches positive infinity. This entire expression is basically going
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to behave as the value of X itself would.
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So it's X gets a very very large X or
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this expression this limit is also going to get very
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very large. So as X approaches infinity, we
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expect this function to approach infinity. Here on the
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graph. I have the function graft. And you
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can clearly see that as as X approaches positive infinity
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, the function is approaching positive infinity. Okay,
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we can zoom out and you can see the more
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and more you move to the right as X approaches
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positive infinity are the function is getting higher and higher
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. So as X approaches positive infinity, our function
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approaches positive infinity, and that's why our function has
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an infinite limit. The limit of our function as
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X approaches infinity is infinity.