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Unformatted text preview: /_\ y = dy = f'(x) dx /_\ z = dz = fx(x,y)dx + fy(x,y) dy- Use the differentials to estimate the max error in calculating the surface area of the box. Approximate surface area: /_\s ~ ds = Sx . dx + S y . dy + S z . dz s = 2xy + 2yz + 2xz w = f(x,y,z) /_\w ~ dw = fx . dx + fy . dy + fz . dz Sx = 2y+2z | (80,60,50) = 220 Sy = 2x + 2z | (80,60,50) = 260 S z = 2y+2x | (80,60,50) = 280 /_\ ~ ds = 220 (0.2) + 260(.2) + 280 (0.2) = 152 cm 2 S = 2xy + 2yz + 2xz Note: /_\x = dx /_\y = dy /_\z = dz-To measure change in surfaces, we use differentials....
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