Questions from General Calculus


Q: Find the area of the region bounded by the given curves.

Find the area of the region bounded by the given curves.

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Q: Find the volume of the solid obtained by rotating the region bounded

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

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Q: An observer stands at a point P, one unit away from

An observer stands at a point P, one unit away from a track. Two runners start at the point S in the figure and run along the track. One runner runs three times as fast as the other. Find the maximum...

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Q: The velocity of a wave of length L in deep water is

The velocity of a wave of length L in deep water is where K and C are known positive constants. What is the length of the wave that gives the minimum velocity?

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Q: A metal storage tank with volume V is to be constructed in

A metal storage tank with volume V is to be constructed in the shape of a right circular cylinder surmounted by a hemisphere. What dimensions will require the least amount of metal?

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Q: 1. If f and g are continuous on [a,

1. If f and g are continuous on [a, b], then 2. If f and g are continuous on [a, b], then 3. If f is continuous on [a, b], then 4. If f is continuous on [a, b], then 5. If f is continuous on [...

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Q: Find the local and absolute extreme values of the function on the

Find the local and absolute extreme values of the function on the given interval.

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Q: Use Newton’s method to find all roots of the equation sin x

Use Newton’s method to find all roots of the equation sin x = x2 – 3x + 1 correct to six decimal places.

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Q: Find f (x). f'(t) = 2t

Find f (x). f'(t) = 2t - 3 sin t, f (0) = 5

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Q: Find f (x). f' (u) = u2

Find f (x). f' (u) = u2 + √u /u, f (1) = 3

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