Questions from General Calculus


Q: Find the volume of the solid in the first octant bounded by

Find the volume of the solid in the first octant bounded by the cylinder z = 16 - x2 and the plane y = 5.

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Q: Find the average value of f over the given rectangle.

Find the average value of f over the given rectangle. f (x, y) = x2y, R has vertices (-1, 0), (-1, 5), (1, 5), (1, 0)

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Q: Find the average value of f over the given rectangle.

Find the average value of f over the given rectangle. f (x, y) = ey √(x + e^y ), R = [0, 4] × [0, 1]

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Q: Use symmetry to evaluate the double integral. ∬R xy

Use symmetry to evaluate the double integral. ∬R xy/(1+ x^4 ) dA, R = {(x, y) | -1 < x < 1, 0 < y < 1}

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Q: Each of these extreme value problems has a solution with both a

Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint....

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Q: Use Lagrange multipliers to give an alternate solution to the indicated exercise

Use Lagrange multipliers to give an alternate solution to the indicated exercise in Section 14.7. Exercise 50 14.7 Exercise 50: Find the dimensions of the rectangular box with largest volume if the...

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Q: Use symmetry to evaluate the double integral. ∬R (

Use symmetry to evaluate the double integral. ∬R (1 + x2 sin y + y2 sin x) dA, R = [-π, π ] × [-π, π]

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Q: A contour map is shown for a function f on the square

A contour map is shown for a function f on the square R = [0, 4] × [0, 4]. (a). Use the Midpoint Rule with m = n = 2 to estimate the value of ∬R f (x, y) dA. (b). Estim...

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Q: Evaluate the iterated integral. ∫_1^5 ∫_0

Evaluate the iterated integral. ∫_1^5 ∫_0^x (8x - 2y) dy dx

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Q: Evaluate the double integral. ∬D y √(x^

Evaluate the double integral. ∬D y √(x^2- y^2 ) dA, D = {(x, y) | 0 < x < 2, 0 < y < x}

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