# Calc05_1 - 5.1 Estimating with Finite Sums 320 miles 50...

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5.1 Estimating with Finite Sums

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320 miles 50 ft/sec 12,000 gallons -3
0 1 2 3 1 2 3 4 time velocity After 4 seconds, the object has gone 12 feet. Consider an object moving at a constant rate of 3 ft/sec. Since rate . time = distance: If we draw a graph of the velocity, the distance that the object travels is equal to the area under the line. ft 3 4 sec 12 ft sec = 3 t d =

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0 1 2 3 1 2 3 4 If the velocity is not constant, we might guess that the distance traveled is still equal to the area under the curve. (The units work out.) 2 1 1 8 V t = + Example: We could estimate the area under the curve by drawing rectangles touching at their left corners. This is called the Left-hand Rectangular Approximation Method (LRAM). 1 1 1 8 1 1 2 1 2 8 t v 1 0 1 1 1 8 2 1 1 2 3 1 2 8 Approximate area: 1 1 1 3 1 1 1 2 5 5.75 8 2 8 4 + + + = =
Method (RRAM). 1

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Calc05_1 - 5.1 Estimating with Finite Sums 320 miles 50...

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