Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y² − x² + 2 and above the rectangle_R = [−1, 1] × [1, 3]. 200 3 X

Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find the volume of the se

A: Given, the curve                   y2(a+x)=x2(a-x)

Q: Find the area of the cap cut from the paraboloid y^2+z^2=2x by the plane x=2

A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

Q: Find the surface area of the portion of 4x + 3y + 5z = 8 that lies inside the cylinder x² + y² = 49.

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Q: A certain parabolic monument has a base that is a parabola ( y=−.5x2+8y=−.5x2+8 ) And a front…

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Q: 6. The figure shows the surface created when the cylinder y² +2²=1 intersects the cylinder ²+²=1.…

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Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx