Questions from General Calculus

Q: (a). Use the Midpoint Rule for double integrals (see

(a). Use the Midpoint Rule for double integrals (see Section 15.1) with four squares to estimate the surface area of the portion of the paraboloid z = x2 + y2 that lies above the square [0, 1] × [0, 1...

Q: Find the exact area of the surface z = 1 + 2x

Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 < x < 4, 0 < y < 1.

Q: Find the exact area of the surface z = 1 + x

Find the exact area of the surface z = 1 + x + y + x2 -2 < x < 1 -1 < y < 1 Illustrate by graphing the surface.

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

Find the area of the surface. The part of the plane 6x + 4y + 2z = 1 that lies inside the cylinder x2 + y2 = 25

Q: Show that the area of the part of the plane z =

Show that the area of the part of the plane z = ax + by + c that projects onto a region D in the xy-plane with area A (D) is √(a^2 + b^2 + 1) A (D).

Q: If you attempt to use Formula 2 to find the area of

If you attempt to use Formula 2 to find the area of the top half of the sphere x2 + y2 + z2 = a2, you have a slight problem because the double integral is improper. In fact, the integrand has an infin...

Q: (a). Find the maximum value of f (x1,

(a). Find the maximum value of f (x1, x2, . . . , xn) = √(n&x_1 x_2…x_n ) given that x1, x2, . . ., xn are positive numbers and x1 + x2 + ∙...

Q: Use a computer algebra system to find the mass, center of

Use a computer algebra system to find the mass, center of mass, and moments of inertia of the lamina that occupies the region D and has the given density function. D is enclosed by the right loop of t...

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Inside both the cylinder x2 + y2 = 4 and the ellipsoid 4x2 + 4y2 + z2 = 64

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

Find the volume of the given solid. Bounded by the planes z = x, y = x, x + y = 2, and z = 0