WEBVTT
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And this question we're going to approximate the slope of
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the tangent line at point B. By approaching point
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P. From another point Q. And then calculating
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the slip of second line peak you And getting the
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X. here smaller and smaller and closer to.5
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. That we will be able to approximate the tangent
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line. The slope of the tangent line at P
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. So for that our first sub question We have
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X equals zero. And that makes her cute zero
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comma co sign of by comma zero. uh by
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time zero which is zero times cosine of zero which
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is one. And that gives us a slope of
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one minus 0/0 minus 10.5. Using the slope formula
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here. And that would be negative too. For
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our second sub question we have X equals 0.4 and
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plugging that into Q. Here we have q equaling
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0.4 comma co sign of pi times 0.4. Which
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when we plug into the calculator We get zero three
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09. Using the slope formula here again, Her
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slope would be zero 309 0 Over.4-15 Which
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is negative 3.09. For a third question, X
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is equal to 0.49. We're getting closer. Rx
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is getting closer and closer to.5. Uh marquis
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was going to be.49 comma co sign of thai
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times 49.49 which is using the calculator 3.0314.
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And that gives us a slow both negative three point
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one for using the steps. The Question one and
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2 For our 4th question Our X is equal to
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zero four 99. Whoops. Yeah, so we
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get a cube of 0.499 comma co sign of play
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time. 0.499 which is 3.14 times 10. Raised
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to-3. And that gives us a slope of
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negative 3.14. Again for question five Our X is
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equal to one that gives us a queue of one
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comma co sign of pie which is negative one.
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And that's a slope of negative 1 0 Over 1
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-15 which is negative two for question six. Our
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X is equal to.6. That gives us a
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queue of 0.6 comma co sign of pi times 0.6
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which is negative zero point There is 09. Mhm
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. And so our slope is going to be negative
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zero 30,990 Divided by.6-15 Which is negative 3.09
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for our seventh question X is equal to 0.51.
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That gives us a queue of 0.51 comma co sign
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of High time, 0.51 which is 0.0 314,
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Point 0314. And that gives us a slow bus
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negative 3.14. Notice how the slope values that we
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were getting after Question five for question 5 6 and
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seven are mirroring the Slips slope values for question 1
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, 2, three and four For question eight similarly
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Um X is equal to 0.501. And so our
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Q. Is going to be is your point 501
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comma coastline of pi times 0.5 0 1. Which
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is going to be-3.14 Times 10 raised-3.
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That gives us a slope of negative 3.14. So
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notice how as we're getting closer and closer two and
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X equals 2.5 or slope is approaching negative 3.14 or
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Pie. So negative pi would be the slope of
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are tangent line act.5. Just be for the
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equation of our change of mind. The formula bertha
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blind prefer is equal to mm times x minus x
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one Plugging the coordinates of p. and the value
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of flow of tangent line into our equation we have
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Y-0 0 is equal to negative pi Times X
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-100. Yeah. Which is why is equal to
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negative pi X plus bye. Yes. Uh huh
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.