Questions from General Calculus

Q: If v = x2 sin y + yexy, where x =

If v = x2 sin y + yexy, where x = s + 2t and y = st, use the Chain Rule to find ∂v/∂s and ∂v/∂t when s = 0 and t = 1.

Q: Suppose z = f (x, y), where x =

Suppose z = f (x, y), where x = g (s, t), y = h (s, t), t (1, 2) = 3, gs (1, 2) = -1, gt (1, 2) = 4, h (1, 2) = 6, hs (1, 2) = -5, ht (1, 2) = 10, fx (3, 6) = 7, and fy (3, 6) = 8. Find ∂z/∂s and ∂z/∂...

Q: Use a tree diagram to write out the Chain Rule for the

Use a tree diagram to write out the Chain Rule for the case where w = f (t, u, v), t = t (p, q, r, s), u = u (p, q, r, s), and v = v (p, q, r, s) are all differentiable functions.

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: If z = y + f (x2 - y2), where

If z = y + f (x2 - y2), where f is differentiable, show that Y ∂z/∂x + ∂z/∂y + = x

Q: If f (x, y) = sin x + sin

If f (x, y) = sin x + sin y, then -√2 A metal plate is situated in the xy-plane and occupies the rectangle 0 (a). Estimate the values of the partial derivatives Tx (6, 4) and Ty (...

Q: If f (x, y) = ln y, then

If f (x, y) = ln y, then ∆f (x, y) = 1/y. Evaluate the limit or show that it does not exist. lim┬((x,y)→(1,1))2xy/(x^2+2y^2 )

Q: Make a rough sketch of a contour map for the function whose

Make a rough sketch of a contour map for the function whose graph is shown. If f has a local minimum at (a, b) and f is differentiable at (a, b), then =f (a, b) = 0.

Q: If (2, 1) is a critical point of f

If (2, 1) is a critical point of f and fxx (2, 1) fyy (2, 1) < [ fxy (2, 1)]2 Evaluate the limit or show that it does not exist. lim┬((x,y)→(1,1))2xy/(x^2+2y^2 )

Q: If f (x, y) has two local maxima,

If f (x, y) has two local maxima, then f must have a local minimum. Find a linear approximation to the temperature function T (x, y) in Exercise 11 near the point (6, 4). Then use it to estimate the...