Questions from General Calculus

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

Find all second partial derivatives of f. f (x, y, z) = xkylzm

Q: Suppose that f is continuous on a disk that contains the point

Suppose that f is continuous on a disk that contains the point (a, b). Let Dr be the closed disk with center (a, b) and radius r. Use the Mean Value Theorem for double integrals (see Exercise 58) to s...

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 all second partial derivatives of f. v = r

Find all second partial derivatives of f. v = r cos (s + 2t)

Q: If z = xy + xey/x, show that x

If z = xy + xey/x, show that x∂z/∂x + y ∂z/∂y = xy + z.

Q: If z = sin (x + sin t), show that

If z = sin (x + sin t), show that

Q: Sketch the graph of the function. f (x,

Sketch the graph of the function. f (x, y) = 1 - y2

Q: Find du if u = ln (1 + se2t).

Find du if u = ln (1 + se2t).

Q: Find the linear approximation of the function f (x, y

Find the linear approximation of the function f (x, y, z) = x3 √(y^2+ z^2 ) at the point (2, 3, 4) and use it to estimate the number (1.98)3 √((3.01)^2 + (3.97)^2 ).

Q: If u = x2y3 + z4, where x = p +

If u = x2y3 + z4, where x = p + 3p2, y = pep, and z = p sin p, use the Chain Rule to find du/dp.