How to Calculate Uncertainty Errors in Derived Quantities?

[a8281333]

After measurements, the following values and their uncertainties were recorded:

x = 8.3 ± 0.1 and y = 2.72 ± 0.07

Find the following values of Z

a) Z = x + y

b) Z = x - y

c) Z = xy

d) Z = x/y

e) Z = y/[(x)^0.5] (this is y divided by the square root of x)

f) Z = exp(y)

g) Z = ln(x + y)

h) tan(x/y)

My attempts: a) 11.02 ± 0.17 ; b) 5.4 ± 0.2 ; c) 22.576 ± 0.007 ; d) 3.1 ± 1.4 ; e) 0.94 ± 0.22 ; f) exp(2.72 ± 0.07) ; g) ln(11.02 ± 0.17) ; h) tan(3.1 ± 1.4)

Any help would be appreciative, I'm a bit rusty, having not done any physics in two years, and apparently, my attempts are all incorrect!

 

[Dale]

Here is a good page that explains the theory and has links at the bottom to many special cases.

http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm

 

[a8281333]

Thank you, I'll have a read of that, I have a recommended textbook entitled measurements and their uncertainties, but it doesn't have any of this fundamental stuff in, I'm finding it really annoying! :(

 

[a8281333]

No more help guys?