Math1011_Week13-1

# Math1011_Week13-1 - Math1011 Section 5.1 The velocity graph...

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Math1011 Section 5.1 11/15/2010 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 1 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 #1011w.51.01)
Math1011 Section 5.1 2 The velocity graph of a snail accelerating from rest to a speed of 3cm/minute over a period of 3 minutes is shown. Use the midpoint rule with 3 rectangles to estimate the area. 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Speed cm/min minutes Use the above calculation to estimate the average value of the function.

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Math1011 Section 5.1 2 The velocity graph of a snail accelerating from rest to a speed of 3cm/minute over a period of 3 minutes is shown. Use the midpoint rule with 3 rectangles to estimate the area. 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 min min min 3 3 min Midpoints: (0.5) 0.7 (1.5) 1.8 (2.5) 2.3 (1min)[(0.7 1.8 2.3) (1min)[4.8 ] 4.8 The snail crawled 4.8 cm in the three minutes.
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