In the following equations, x, y, and z are measured quantities and each has its uncertainty. Write the expressions of the absolute and relative uncertainty for 1. A = x - y - z
Write the expressions for relative uncertainties for the following functions:
2. B = 1/x
3. C = x * y * z
4. D = 5x^2
5. E = (x/y)^(1/2)
6. F = (x + y)/(x - y)
7. G = (x + y)z
8. H = sin x
For functions F and G, it may be simpler to replace the quantities in the parenthesis by a single letter first, e.g. J = x + y, K = x - y, so F = J/K, G = Jz. Then calculate the uncertainties of J and K before calculating the uncertainties in F and G.
Three quantities are measured, x = 10.30 ± 0.05, y = 2.51 ± 0.03, and z = 0.384 ± 0.002. Calculate the quantities and their uncertainties of A and D. Express the results in standard form.