5.1 Estimating with Finite Sums
y = 0.5(x­1)2+1
Approximate the area under the curve using a Left­hand Rectangular Approximation Method with 4 subintervals. Is the approx. an under or overestimate?
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2
y = 0.5(x­1) +1
Right­hand Rectangular Approximation Method
2
y = 0.5(x­1)2+1
Midpoint Rectangular Approximation Method
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Use RAM with 6 partitions to estimate the area of the region enclosed between the graphs of g and the x­axis for 0≤x≤3.
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Suppose you were walking at a constant rate of 3 feet per second.
velocity
How far have your gone after 4 seconds (distance traveled)?________ Can you make any connections between the graph of the velocity function and your total distance traveled?
time
Now suppose you were not walking at a constant rate.
velocity
How far have your gone after 4 seconds (distance traveled)?________ time
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Does the same hold true for a position function? Find the distance traveled for each graph shown.
meters
yards
feet
sec
min
hr
Find a velocity graph for each position and analyze the results.
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The number of cars per hour passing an observation point along a highway is called the rate of traffic flow r(t) (in cars per hour).
t
7:00
7:15
8:30
8:45
9:00
r(t)
1,044
1,297 1,478 1,844 1,451 1,378 1,155
802
542
7:30
7:45
8:00
8:15
a) What does represent? b) The flow rate is recorded at 15­min intervals between 7:00 and 9:00 AM. Estimate the number of cars using the highway during this 2­hour period by taking the average of the left and right­endpoint approximations.
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