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Math1011_Week12_48_51234

# Math1011_Week12_48_51234 - Math1011 Section 5.1 The...

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Math1011 Section 5.1 11/18/2009 The velocity graph of a snail accelerating from rest to a speed of 3cm/minute over a period of 3 minutes is shown. Provide an underestimate and an overestimate for the distance traveled during this period. Draw approximating rectangles for both. Calculate/Draw an underestimate for the area (3 rectangles) 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Calculate/Draw an overestimate for the area (3 rectangles) 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Speed cm/min minutes Speed cm/min minutes

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Math1011 Section 5.1 11/18/2009 The velocity graph of a snail accelerating from rest to a speed of 3cm/minute over a period of 3 minutes is shown. Provide an underestimate and an overestimate for the distance traveled during this period. Draw approximating rectangles for both. Calculate/Draw an underestimate for the area 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 3 min min min 3 min Increasing functions: left endpoints underestimate. (1min)[(0 1.4 2.1 ) (1min)[3.5 ] 3.5 The snail crawled at least 3.5cm in the three minutes. cm cm cm cm L L c = + + = = m Calculate/Draw an overestimate for the area 0 0.5 1 1.5 2 2.5 3 0 0.5 Speed cm/min minutes 3 min min min 3 min Increasing functions: right endpoints overestimate. (1min)[(1.4 2.1 2.4 ) (1min)[5.9 ] 5.9 The snail crawled at most 5.9cm in the three minutes. cm cm cm cm R R c = + + = = 1 1.5 2 2.5 3 m Speed cm/min minutes (Doc #011w.51.01t)
Math1011 Section 5.1 2 The speed of a runner is increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find the lower and upper sums. What do the lower and upper sums represent? t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v(ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2

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Math1011 Section 5.1 2 The speed of a runner is increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find the lower and upper sums. What do the lower and upper sums represent?
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