tailieunhanh - Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 87

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 87. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Finding Mass When Density Varies 841 b Another truffle is made in a hemispherical mold with radius R. Layers of different types of chocolate are poured into the mold one at a time and allowed to set. The number of calories per cubic millimeter varies with x where x is the depth from the top of the mold. The calorie density is given by x calories mm3. Write an integral that gives the number of calories in this hemispherical truffle. Top of the mold Hemispherical truffle mold 14. Liquid is being stored in a large spherical tank of radius 2 meters. The tank is completely full and has been left standing for a long time. A mineral suspended in the liquid is setting. Its density at a depth of h meters from the top is given by 5h milligrams per cubic meter. Determine the number of milligrams of the mineral contained in the tank. Top 15. A circular pond is 60 meters in diameter and has a bridge running along a diameter. At lunchtime people stand on the bridge and throw bread onto the water to feed the ducks. As a result the density of ducks on the pond is given by a function p x ducks per square meter where x is the distance from the bridge. How many ducks are on the pond We will assume that the bridge itself is very thin so we can ignore its width. Notice that we cannot really say that the ducks are continuously distributed on the pond. Ducks after all are discrete. We are making a continuous model of a discrete phenomenon. 16. Let W t be the amount of water in a pool at time t t measured in hours and W measured in gallons. t 0 corresponds to noon. Water is flowing in and out of the pool at a rate given by W 30 cos 2t . During what time interval between noon and 5 00 . 0 t 5 is water flowing out of the pool at a rate of 15 gallons an hour or more How much water actually has left the pool in this time interval 17. In the town of Lybonrehc there has been a nuclear reactor meltdown which released radioactive iodine 131. Fortunately the reactor has a containment .

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