Questions from General Calculus


Q: An agricultural sprinkler distributes water in a circular pattern of radius 100

An agricultural sprinkler distributes water in a circular pattern of radius 100 ft. It supplies water to a depth of e2r feet per hour at a distance of r feet from the sprinkler. (a). If 0 < R < 100, w...

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Q: (a). If your computer algebra system plots implicitly defined curves

(a). If your computer algebra system plots implicitly defined curves, use it to estimate the minimum and maximum values of f (x, y) = x3 + y3 + 3xy subject to the constraint (x – 3)2 + (y – 3)2 = 9 by...

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Q: Prove Property 11. Property 11: /

Prove Property 11. Property 11:

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Q: Find the average value of the function f (x, y

Find the average value of the function f (x, y) = 1/√(x^2 + y^2 ) on the annular region a2 < x2 + y2 < b2, where 0 < a < b.

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Q: Use geometry or symmetry, or both, to evaluate the double

Use geometry or symmetry, or both, to evaluate the double integral. ∬D (x + 2) dA, D = {(x, y) | 0 < y < √(9 - x^2 )

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Q: Use geometry or symmetry, or both, to evaluate the double

Use geometry or symmetry, or both, to evaluate the double integral. ∬D √(R^2-x^2-y^2 ) dA, D is the disk with center the origin and radius R

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Q: Use geometry or symmetry, or both, to evaluate the double

Use geometry or symmetry, or both, to evaluate the double integral. (2x + 3y) dA, D is the rectangle 0 < x < a, 0 < y < b

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Q: Use geometry or symmetry, or both, to evaluate the double

Use geometry or symmetry, or both, to evaluate the double integral. ∬D (2 + x2y3 - y2 sin x) dA, D = {(x, y) | |x | + |y | < 1j

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Q: Use geometry or symmetry, or both, to evaluate the double

Use geometry or symmetry, or both, to evaluate the double integral. ∬D (ax3 + by3 + √(a^2 - x^2 ) d dA, D = [-a, a] × [-b, b]

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Q: Graph the solid bounded by the plane x + y + z

Graph the solid bounded by the plane x + y + z = 1 and the paraboloid z = 4 - x2 - y2 and find its exact volume. (Use your CAS to do the graphing, to find the equations of the boundary curves of the r...

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