University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

354

Pages:

1
Author:

beddgell23k

Workshop #16 ∂F 1. If F (s, t) = f (x, y) = f (x(s, t), y(s, t)), find an expression for . List all possible first derivatives ∂s that can be found in this problem. 2. If F (x, y, z) = f (t, u, w) = f (t(x, z), u(x, y), w(z)), list all possible first derivatives that can be found in this problem. Find expressions for the first derivative of F with respect to x, the first derivative of F with respect to y, and the first derivative of F with respect to z. 3. If F (t) = f (u, v) with u = g(t) and v = h(t), what function values do you need to know so that you dF can evaluate F (2)? To evaluate ? dt t=2 4. If F (t, s) = f (u, v) with u = g(t, s) and v = h(t, s), what function values do you need to know so ∂F ? that you can evaluate F (2, 3)? To evaluate ∂t (2,3) 5. Suppose that f is a differentiable function of x and y and g(r, s) = f (2r2 − s2 , r + 3s). Calculate gr (2, 3) and gs (2, 3), given the values below. (-1,11) (2,3) f 2 -2 g 5 3 fx 4 -1 fy 7 6