WEBVTT
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So here we are going to graph the function sign
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x minus Sign of 1000 X. All over 1000
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. And then observe it in different viewing rectangles.
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And Try to observe what the slope at zero is
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. So I've taken the first bounds-2 pi to
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pie And-4- four. Those are X and
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Y bounds respectively. And so it looks something like
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this here. I'm using Dismas but you can use
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your graphing calculator, your own graphing calculator or any
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other graphing utility you have. And so it looks
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like a zero. We have a pretty straight line
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that goes from negative one negative 1 to 1 comma
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one. So we can approximate the slope to be
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about one. So we're going to say the slope
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is about one. Now we have to change our
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bounds to these values. So I can do that
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in Desmond's here by using this graph settings button and
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changing the X axis bounds the ones we need and
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are Y axis bones similarly. And so now can
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see that it's a little different or you can see
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but it's not your typical sine function, there is
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a little bit of a squiggle going on and so
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line very close to the origin is kind of hard
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to see from here. Well assuming just a tiny
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bit and it looks like it goes flat just right
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where it hits the origin. So let's go ahead
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and approximate This answer. This slope as zero which
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of course does not agree with our answer from party
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. And then we're going to zoom in one last
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time here To negative 0.008 And positive 0.008 and the
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Y axis we have 0.005. And as you can
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see where we kind of zoomed in on the squiggle
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now and you can see that Very clearly hit zero
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at or the slope it looks like it has an
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inflection point at the origin. So we can confirm
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our estimate That the slope is approximately zero my observation
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at the origin.