- #1
Oerg
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Homework Statement
Given that [tex] f=\frac{\bar u \bar v}{\bar u +\bar v}[/tex]
show that
[tex]e_f=f^2({\frac{e_u}{\bar u^2} + \frac{e_v}{\bar v^2}) [/tex]
where [tex]e[/tex] refers to the error. ok so I added up the fractional uncertainties
Homework Equations
The Attempt at a Solution
and I got this
[tex]\frac{e_f}{f}=\frac{e_u}{u}+\frac{e_v}{v}+\frac{e_u+e_v}{u+v}[/tex]
after some simplifying, I got to this,
[tex]e_f=f^2(\frac{e_u(u+v)}{u^2v}+\frac{e_v(u+v)}{v^2u}+\frac{e_u+e_v}{uv})[/tex]
and then I realized that I could never get the answer, however, if this term was negative,
[tex]\frac{e_u+e_v}{uv}[/tex], i would get the answer perfectly, but how can it be negative? Problem is even in division, shouldn't the fractional uncertianties add up??