WEBVTT
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So in this problem were given The speedometer readings at
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10 2nd intervals during a one minute period for a
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racing car. And so we have that table of
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those. Okay. Were used to estimate the distance
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the car traveled. Using the velocities at the beginning
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of intervals that has to do it again using the
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loss at the end of the intervals. And then
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we are asked uh our estimates in estimates in parts
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A and B. Upper and lower estimates. Well
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let's think about this for a minute. If this
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is our graph of our data, think of something
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like this. Okay. And we draw in these
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rectangles that are going to use the left side of
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the curve like so okay, be like this right
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all the time. That means that the laughter of
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the beginning. Okay, the beginning are going to
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be the lower sums and the ending ones then are
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going to be the upper sums our estimates. Okay
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, so that's how that's going to work for us
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. So let's look at the data now. So
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we are given this set of data right here.
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I just piped it into a little spreadsheet real quick
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right here, Time from 0 to 60 seconds and
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our velocity of the speedometer and miles per second.
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His shows are 18, 168 and so on.
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Okay, So I know each of these intervals is
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10 seconds. So whatever delta T is 10.
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So then taking the 10 times the beginning. So
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I mean is this first one b 10 times the
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1 82.9. Is this the 1829? And so
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the next 10 it becomes the 168 would be that
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one? Okay. That gives us the lower sums
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of 87, 79. Course, this is in
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miles. And then the upper sums, yeah.
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Would be the ones on the ending right over here
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. Okay. And that 10 miles. Okay?
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We can see the difference between the two and we
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see which ones are the lower and which ones are
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the upper sums.