Questions from General Calculus

Q: Find the volume of the given solid. Find the volume

Find the volume of the given solid. Find the volume of the given solid. Bounded by the cylinder x2 + y2 = 4 and the planes z = 0 and y + z = 3

Q: Find the volume of the given solid. One of the

Find the volume of the given solid. One of the wedges cut from the cylinder x2 + 9y2 = a2 by the planes z = 0 and z = mx

Q: Find the volume of the given solid. Above the paraboloid

Find the volume of the given solid. Above the paraboloid z = x2 + y2 and below the half-cone z = √(x^2 + y^2 )

Q: Consider a lamina that occupies the region D bounded by the parabola

Consider a lamina that occupies the region D bounded by the parabola x = 1 - y2 and the coordinate axes in the first quadrant with density function ρ (x, y) = y. (a). Find the mass of the lamina. (b)....

Q: A lamina occupies the part of the disk x2 + y2 <

A lamina occupies the part of the disk x2 + y2 < a2 that lies in the first quadrant. (a). Find the centroid of the lamina. (b). Find the center of mass of the lamina if the density function is ρ (x, y...

Q: (a). Find the centroid of a solid right circular cone

(a). Find the centroid of a solid right circular cone with height h and base radius a. (Place the cone so that its base is in the xy-plane with center the origin and its axis along the positive z-axis...

Q: (a). When is the directional derivative of f a maximum

(a). When is the directional derivative of f a maximum? (b). When is it a minimum? (c). When is it 0? (d). When is it half of its maximum value?

Q: Find the extreme values of f subject to both constraints.

Find the extreme values of f subject to both constraints.

Q: Find the area of the part of the surface z = x2

Find the area of the part of the surface z = x2 + y that lies above the triangle with vertices (0, 0), (1, 0), and (0, 2).

Q: Graph the surface z = x sin y, -3 <

Graph the surface z = x sin y, -3 < x < 3, -π < y < π, and find its surface area correct to four decimal places.