Questions from General Calculus

Q: Let f (x, y) = xey + x4y +

Let f (x, y) = xey + x4y + y3. Find ∂2f/∂x2, ∂2f/∂y2, ∂2f/∂x∂y, and ∂2f/∂y∂x.

Q: A farmer can produce f (x, y) = 200

A farmer can produce f (x, y) = 200 √(6x2 + y2) units of produce by utilizing x units of labor and y units of capital. (The capital is used to rent or purchase land, materials, and equipment.) (a) Cal...

Q: The productivity of a country is given by f (x,

The productivity of a country is given by f (x, y) = 300x2/3y1/3, where x and y are the amount of labor and capital. (a) Compute the marginal productivities of labor and capital when x = 125 and y = 6...

Q: Find ∂f/∂x and ∂f/∂y for each

Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = 5xy

Q: Find ∂f/∂x and ∂f/∂y for each

Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = x2 - y2

Q: Find ∂f/∂x and ∂f/∂y for each

Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = 2x2ey

Q: Let f (x, y) = xy. Show that

Let f (x, y) = xy. Show that f (2, 3 + k) - f (2, 3) = 2k.

Q: Find ∂f/∂x and ∂f/∂y for each

Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = x exy

Q: Find ∂f/∂x and ∂f/∂y for each

Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = x/y + y/x

Q: Find ∂f/∂x and ∂f/∂y for each

Find ∂f/∂x and ∂f/∂y for each of the following functions. f (x, y) = 1/(x + y)