Answer:
The maximum error in the function G, ΔG = ±4
Step-by-step explanation:
G(x,y,z) = 20 In (xyz²)
Total or maximum error for a multi-variable function is given by
ΔG = (∂G/∂x) (Δx) + (∂G/∂y) (Δy) + (∂G/∂z) (Δz)
(∂G/∂x) = 20yz²/xyz² = 20/x
(∂G/∂y) = 20xz²/xyz² = 20/y
(∂G/∂z) = 40xyz/xyz² = 40/z
Δx = ±0.10
Δy = ±0.15
Δz = ±0.20
ΔG = (∂G/∂x) (Δx) + (∂G/∂y) (Δy) + (∂G/∂z) (Δz)
ΔG = (20/x) (0.10) + (20/y) (0.15) + (40/z) (0.2)
At the point (x,y,z) = (2,3,4)
ΔG = (20/2) (0.10) + (20/3) (0.15) + (40/4) (0.2) = 10(0.10) + 20(0.05) + 10(0.2) = 1 + 1 + 2 = 4
ΔG = ±4
