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Propagation of error

Find error in w:

(1) w = x + 2y - 3z = 14

(2) w = 2t - 3e = -115

(3) w = x * 2y * 3z = 600

(4)w = 2x/2y = x/y = 2

(5) w = 1/8 (1/y) + ¾ (z/x) + ¼ (y/x) = 0.3

(6) w = 2 (y/z) - 3(x/z) = -10

(7) w=ycost = 4.92

(8) w = t2/sin t = v1 / v2 = 575.877

(9) w = tan t / tan e = 0.1763
(10)w = x3 / cos e = v1/v2 = 1414.2136
(11) w = ln x = 2.303
(12) w=ln (x/3y2) = -2.0149
(13) w = 3 x-2 + 5 y-3
(14)w = (x3 + 3y/z2) ½ = 31.682

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For all the calculations I have used the following general rules for calculating the propagation of error.

w = x +/- y, dw = dx +/- dy

w = xy or x/y, dw/w = dx/x + dy/y

w= xmyn , dw/w = |m| dx/x + |n| dy/y

w = f(x,y), dw = |f/x| dx + |f/y| dy

(1)

w = x + 2y - 3z = 14
dw = dx + 2dy + 3dz = 3.6
% error = dw/w *100 = 25.7%

(2)

w = 2t - 3e = -115
dw = 2dt + 3de = 14
% error = dw/w *100 = 12.2%

(3)
w = x * ...

Solution Summary

I have calculated the error in 14 different functions, which involves sine, cosine, ln and tan functions. I consider this problem set to be a great practice problem set for students who are taking physics/Engineering laboratory.

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