Questions from General Calculus


Q: The air in a room with volume 180 m3 contains 0.

The air in a room with volume 180 m3 contains 0.15% carbon dioxide initially. Fresher air with only 0.05% carbon dioxide flows into the room at a rate of 2 m3ymin and the mixed air flows out at the sa...

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Q: A vat with 500 gallons of beer contains 4% alcohol (

A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min and the mixture is pumped out at the same rate. What is the percentag...

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Q: A tank contains 1000 L of pure water. Brine that contains

A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tan...

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Q: When a raindrop falls, it increases in size and so its

When a raindrop falls, it increases in size and so its mass at time t is a function of t, namely, m(t). The rate of growth of the mass is km(t) for some positive constant k. When we apply New ton’s La...

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Q: (a) Approximate f by a Taylor polynomial with degree n

(a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor’s Inequality to estimate the accuracy of the approximation / when x lies in the given interval....

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Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.

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Q: An object of mass m is moving horizontally through a medium which

An object of mass m is moving horizontally through a medium which resists the motion with a force that is a function of the velocity; that is, where v = v(t) and s = s(t) represent the velocity and po...

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Q: Allometric growth in biology refers to relationships between sizes of parts of

Allometric growth in biology refers to relationships between sizes of parts of an organism (skull length and body length, for instance). If L1(t) and L2(t) are the sizes of two organs in an organism o...

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Q: A model for tumor growth is given by the Gompertz equation

A model for tumor growth is given by the Gompertz equation where a and b are positive constants and V is the volume of the tumor measured in mm3. (a) Find a family of solutions for tumor volume as a f...

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Q: Let A(t) be the area of a tissue culture

Let A(t) be the area of a tissue culture at time t and let M be the final area of the tissue when growth is complete. Most cell divisions occur on the periphery of the tissue and the number of cells o...

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