Find the jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables. if x = f(u, v, w), y = g(u, v, w), and z = h(u, v, w), then the jacobian of x, y, and z with respect to u, v, and w is ∂(x, y, z) ∂(u, v, w) = ∂x ∂u ∂x ∂v ∂x ∂w ∂y ∂u ∂y ∂v ∂y ∂w ∂z ∂u ∂z ∂v ∂z ∂w . spherical coordinates x = ρ sin φ cos θ, y = ρ sin φ sin θ, z = ρ cos φ

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step-by-step explanation:

c

step-by-step explanation:

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step-by-step explanation:

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)