by BlastRoom
Approximating an accumulated quantity from tabulated or graphed rate data with unequal subintervals.
#calculus

24 questions
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Outrun the snow together.
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The class blasts through walls together.
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Sell tours. Nice, standard, or a total scam.
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Sand pours onto a pile, at rate in kilograms per second, with in seconds, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in kilograms.

The figure shows the graph of a RATE against time. Use a LEFT Riemann sum with equal subintervals to approximate the total accumulated over .

As sand pours onto a pile, the rate in kilograms per second gives a left Riemann sum of over . What does that number estimate?
A colony grows, at rate in bacteria per hour, with in hours, as the table shows. Use a RIGHT Riemann sum with the table's three subintervals to approximate the total, in bacteria.

Sand pours onto a pile, at rate in kilograms per second, with in seconds, as the table shows. Use a MIDPOINT approximation on the ONE subinterval , with height .

As sand pours onto a pile, the rate in kilograms per second gives a left Riemann sum of over . What does that number estimate?
Water flows into a tank, at rate in gallons per minute, with in minutes, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in gallons.

The figure shows the graph of a RATE against time. Use a LEFT Riemann sum with equal subintervals to approximate the total accumulated over .

A machine consumes power, at rate in kilowatts, with in hours, as the table shows. Estimate the total energy used, in kilowatt-hours, from t = 0 to t = 8. Use a MIDPOINT approximation on the ONE subinterval .

As a colony grows, the rate in bacteria per hour gives a left Riemann sum of over . What does that number estimate?
Water flows into a tank, at rate in gallons per minute, with in minutes, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in gallons.

Traffic passes a sensor, at rate in cars per minute, with in minutes, as the table shows. Use a RIGHT Riemann sum with the table's three subintervals to approximate the total, in cars.

A colony grows, at rate in bacteria per hour, with in hours, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in bacteria.

As sand pours onto a pile, the rate in kilograms per second gives a left Riemann sum of over . What does that number estimate?
Water flows into a tank, at rate in gallons per minute, with in minutes, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in gallons.

A machine consumes power, at rate in kilowatts, with in hours, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in kilowatt-hours.

Traffic passes a sensor, at rate in cars per minute, with in minutes, as the table shows. Use a RIGHT Riemann sum with the table's three subintervals to approximate the total, in cars.

Water flows into a tank, at rate in gallons per minute, with in minutes, as the table shows. Estimate the total water, in gallons, that flows in from t = 0 to t = 8. Use a MIDPOINT approximation on the ONE subinterval .

A colony grows, at rate in bacteria per hour, with in hours, as the table shows. Estimate the total number of bacteria added from t = 0 to t = 8. Use a MIDPOINT approximation on the ONE subinterval .

A colony grows, at rate in bacteria per hour, with in hours, as the table shows. Use a RIGHT Riemann sum with the table's three subintervals to approximate the total, in bacteria.

A machine consumes power, at rate in kilowatts, with in hours, as the table shows. Use a LEFT Riemann sum with the table's three subintervals to approximate the total, in kilowatt-hours.

The figure shows the graph of a RATE against time. Use a LEFT Riemann sum with equal subintervals to approximate the total accumulated over .

A colony grows, at rate in bacteria per hour, with in hours, as the table shows. Use a RIGHT Riemann sum with the table's three subintervals to approximate the total, in bacteria.

A colony grows, at rate in bacteria per hour, with in hours, as the table shows. Use a RIGHT Riemann sum with the table's three subintervals to approximate the total, in bacteria.

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Over- and Under-estimates
20 questions