Questions from General Calculus

Q: Calculate the iterated integral by first reversing the order of integration.

Calculate the iterated integral by first reversing the order of integration.

Q: Calculate the value of the multiple integral. ∬R yexy

Calculate the value of the multiple integral. ∬R yexy dA, where R = {(x, y) | 0 < x < 2, 0 < y < 3)

Q: Calculate the value of the multiple integral. ∬D xy

Calculate the value of the multiple integral. ∬D xy dA, where D = {(x, y) | 0 < y < 1, y2 < x < y + 2}

Q: Calculate the value of the multiple integral. ∭E y

Calculate the value of the multiple integral. ∭E y/(1+x^2 dA, where D is bounded by y = √x, y = 0, x = 1

Q: Calculate the value of the multiple integral. ∬D 1

Calculate the value of the multiple integral. ∬D 1/(1+x^2 ) dA, where D is the triangular region with vertices (0, 0), (1, 1), and (0, 1).

Q: The method of Lagrange multipliers assumes that the extreme values exist,

The method of Lagrange multipliers assumes that the extreme values exist, but that is not always the case. Show that the problem of finding the minimum value of f (x, y) = x2 + y2 subject to the const...

Q: Find equations of (a) the tangent plane and (b

Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specified point. z = 3x2 - y2 + 2x, (1, -2, 1)

Q: Find equations of (a) the tangent plane and (b

Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specified point. z = ex cos y, (0, 0, 1)

Q: Find equations of (a) the tangent plane and (b

Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specified point. x2 + 2y2 - 3z2 = 3, (2, -1, 1)

Q: Find equations of (a) the tangent plane and (b

Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specified point. xy + yz + zx = 3, (1, 1, 1)