Questions from General Calculus

Q: Pictured are a contour map of f and a curve with equation

Pictured are a contour map of f and a curve with equation t (x, y) = 8. Estimate the maximum and minimum values of f subject to the constraint that t (x, y) = 8. Explain your reasoning.

Q: Each of these extreme value problems has a solution with both a

Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint....

Q: Find the center of mass of the solid tetrahedron with vertices (

Find the center of mass of the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 2, 0), (0, 0, 3) and density function ρ (x, y, z) = x2 + y2 + z2.

Q: Find the first partial derivatives. S (u, v

Find the first partial derivatives. S (u, v, w) = u arctan (v √w)

Q: Find all second partial derivatives of f. f (x

Find all second partial derivatives of f. f (x, y) = 4x3 - xy2

Q: Rewrite the integral as an iterated integral in the order dx dy

Rewrite the integral as an iterated integral in the order dx dy dz.

Q: Give five other iterated integrals that are equal to ∫_0

Give five other iterated integrals that are equal to ∫_0^2 ∫_0^(y^3) ∫_0^(y^2) f (x,y,z) dz dx dy

Q: Use the transformation u = x - y, v = x

Use the transformation u = x - y, v = x + y to evaluate where R is the square with vertices (0, 2), (1, 1), (2, 2), and (1, 3).

Q: Use the transformation x = u2, y = v2, z

Use the transformation x = u2, y = v2, z = w2 to find the volume of the region bounded by the surface √x + √y + √z = 1 and the coordinate planes.

Q: Find all second partial derivatives of f. z = xe

Find all second partial derivatives of f. z = xe-2y