Uncertainty Derivations/Calculation

[tmobilerocks]

Homework Statement

If F = aXⁿ = f +- f +δf where a is a constant, show f = xⁿ and $\frac{δf}{f}$ = $\frac{nδx}{x}$.

X = x +- δx

x refers to the average and δx refers to uncertainty in x.

Homework Equations

The power rule for error propagation shows that the uncertainty is multiplied n times (where n is the power raised).

The Attempt at a Solution

I'm having trouble showing that f = xⁿ. Through the use of algebraic manipulation, I was able to get a(x+δx)ⁿ = f + δf. I then made the assumption to ignore the constant a and by deduction say x = 5 +- 0.5, set f = xⁿ because it is continuously multiplied by whatever the function x is to the nth power. The second part is easier- mainly I just took the differential δf = n*x^n-1δx. This simplifies to $\frac{δf}{f}$ = n$\frac{δx}{x}$

 

[BvU]

Hello t and welcome to PF. If I want to help, I have to be able to read what you've written. Could you proofread your stuff and explain what isn't completely universally known language ?

I recognize some aspects from error propagation theory, but I find your jargon hard to understand.

 

[tmobilerocks]

Hello,

I am supposed to show that f = xⁿ given that F = aXⁿ = f ± δf where a is a constant. X is equal to x ± δx. In plain English, X is equal to the average x, plus or minus the uncertainty in x (δx).

I am having trouble showing that f = xⁿ. I have already derived δf/f using the method shown above.

Thanks again!

 

[BvU]

Yes, it still looks weird that a should disappear from f. Is that really how it is presented to you ?
I mean if F = 1000 X² and X = 5.000 ± 0.001 there is no way that f can be x²