Questions from General Calculus

Q: Find the mass and center of mass of the lamina that occupies

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by y = 1 - x2 and y − 0; ρ (x, y) = ky

Q: Find the mass and center of mass of the lamina that occupies

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by y = x + 2 and y = x2; ρ (x, y) = kx2

Q: Find the mass and center of mass of the lamina that occupies

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by the curves y = e-x, y = 0, x = 0, x = 1; ρ (x, y) = xy

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the plane 5x + 3y = z + 6 = 0 that lies above the rectangle [1, 4] × [2, 6]

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the sphere x2 + y2 + z2 = 4 that lies above the plane z = 1

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the sphere x2 + y2 + z2 = a2 that lies within the cylinder x2 + y2 = ax and above the xy-plane

Q: Find the center of mass of the lamina in Exercise 11 if

Find the center of mass of the lamina in Exercise 11 if the density at any point is proportional to the square of its distance from the origin. Exercise 11: A lamina occupies the part of the disk x2...

Q: Find the maximum and minimum values of f subject to the given

Find the maximum and minimum values of f subject to the given constraints. Use a computer algebra system to solve the system of equations that arises in using Lagrange multipliers. (If your CAS finds...

Q: Find the area of the surface correct to four decimal places by

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = 1/ (1 +...

Q: Find the area of the surface correct to four decimal places by

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = cos (x2...