WEBVTT
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So in this problem were asked to guess the value
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of this limit if it exists by adding the function
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at the given numbers and were given a limit as
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X approaches three of the function X squared minus three
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X over x squared minus nine. Well let's notice
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something here first of all, Notice that this is
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the limit as X approaches three of x times X
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-3 over X plus three times X minus three.
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And so those cancel. And so we have the
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limit As X approaches three of X over X plus
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three which is 3/6, which is one half.
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So expect that these numbers were going to evaluate Will
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all approach 1/2. So now let's see what happens
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. So I have a value of X here and
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the value of my function. Okay I'm asked to
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do this at 3.1 3.5 three points oh one three
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point 001 and three point 0001. Okay so let's
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let's do these right, these are all approaching three
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from the right aren't they? Because their numbers greater
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than three. Okay. So if I go for
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a second to my graphing calculator and I put in
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the function um must do the parentheses X. Weird
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minus three X. Those are differences divided by X
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squared minus nine. Okay. And I look for
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a minute around value three. Let me fix my
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wife scale here for a minute. Go 0-
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one. Okay now Here's three right here. OK
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and there's a half. So you notice that the
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function right, goes right through that half there,
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doesn't it? Right through that half right there.
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Okay. So what I can do is look at
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these values 3.1 3.1 is here is here and I
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need It said to six decimal places. Well let's
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see. I could do is go into my calculator
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. Go 3.1 squared-3 times 3.1. Is that
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divided by Princess? 3.1 squared-9 goes out.
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My breath sees there you go. Can't be right
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to clear all this out. 3.1 squared minus three
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Times 3.1. Is that divided by Princess 3.1?
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33 3.1 squared minus nine. Those princesses that Okay
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, So 508 196 Would be six decimal places or
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197 508197. Okay, so go back over here
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. Back to here. 0.5. What we say
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? 508197 0819 197. Okay, good. 197
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. Okay. And if we put it in as
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305, that in our calculator as well. And
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calculated then what we'll get is 0.5 04 132,
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Putting 301 in there, we'll get 0.500 eight 3
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1. You know this is getting closer and closer
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to.5 and 0.5 0008 three. To make that
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a little bit neater there And then three triple on
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one. A 0.5, 0000 eight. Okay,
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then the next phase were given are 2.9, 2.95
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, 2.99, 2.999, two point 9999. We
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plug those in and calculate them like we did the
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others. You'll get 0.49 15, And then we'll
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get 0.4 95 798 And a zero 499 165.
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And then 0.4999 16, 0.4 999 91. So
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as we can see These are all approaching.5,
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which is a half. So this limit as x
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approaches three is a half.