Questions from General Calculus

Q: The joint density function for random variables X, Y, and

The joint density function for random variables X, Y, and Z is f (x, y, z) = Cxyz if 0 < x < 2, 0 < y < 2, 0 < z < 2, and f (x, y, z) = 0 otherwise. (a). Find the value of the constant C. (b). Find P...

Q: (a). In what way are the theorems of Fubini and

(a). In what way are the theorems of Fubini and Clairaut similar? (b). If f (x, y) is continuous on [a, b] × [c, d] and

Q: Consider the problem of minimizing the function f (x, y

Consider the problem of minimizing the function f (x, y) = x on the curve y2 + x4 - x3 = 0 (a piriform). (a). Try using Lagrange multipliers to solve the problem. (b). Show that the minimum value is f...

Q: Find the moments of inertia Ix, Iy, I0 for the

Find the moments of inertia Ix, Iy, I0 for the lamina of Exercise 15. Exercise 15: Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a if the...

Q: (a). Find the region E for which the triple integral

(a). Find the region E for which the triple integral is a maximum. (b). Use a computer algebra system to calculate the exact maximum value of the triple integral in part (a).

Q: Express D as a union of regions of type I or type

Express D as a union of regions of type I or type II and evaluate the integral. ∬D x2 dA

Q: Find the approximate volume of the solid in the first octant that

Find the approximate volume of the solid in the first octant that is bounded by the planes y = x, z = 0, and z = x and the cylinder y = cos x. (Use a graphing device to estimate the points of intersec...

Q: Use Property 11 to estimate the value of the integral.

Use Property 11 to estimate the value of the integral. ∬S √(4- x^2 y^2 ) dA, S = {(x, y) | x2 + y2 0} Property 11:

Q: Use Property 11 to estimate the value of the integral.

Use Property 11 to estimate the value of the integral. ∬T sin4(x + y) dA, T is the triangle enclosed by the lines y = 0, y = 2x, and x = 1 Property 11:

Q: Find the averge value of f over the region D.

Find the averge value of f over the region D. f (x, y) = xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 3)