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2B_27_9_10 - L e c tu r e 2 S e c t io n 5.1 A r e a s a n...

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Lecture 2 Section 5.1: Areas and Distances
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A car is traveling at 60 feet per second when the driver spots a deer on the road 230 feet ahead and slams on the breaks. 60 40 10 0 Speed (in feet) 0 2 4 6 Time (in seconds) If the deer freezes and does not move, will the car hit the deer? Quiz
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Approximate the area beneath a non-negative function Problem : Approximate the area of the region enclosed by the graph of f, the x-axis and the lines x=a and x=b f(x): non-negative function on [a,b] Answer : approximate the region with N rectangles take the sum of the areas of the N rectangles The bigger is the number N of rectangles, the better is the approximation.
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f(x)=x 2 [a,b]=[0,1] N= # rectangles N=5 N=15 N=50
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Find the (exact value of the) area beneath a non-negative function Problem : Find the area of the region enclosed by the graph of f, the x-axis and the lines x=a and x=b f(x): non-negative function on [a,b] Answer : approximate the region with N rectangles take the sum of the areas of the N rectangles take the limit of the sum as N infinity If f(x) is continuous, this limit exists.
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Problem 1: Approximate the area beneath a non-negative function ~ sum of rectangles estimate Area
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