How Do You Calculate Uncertainty in the Function f(x,z)=z/x?

[glasshut137]

Homework Statement

Calculate "f" and its uncertainty, watch the units, show all work.

Homework Equations

f(x,z)= z/x
x=100.5(+ or -) 3.8 cm
y=71(+ or -) 1 s

The Attempt at a Solution

ok so i know that to find uncertainty i have to use the equation delta f(x,y)=df(x,y)/dx *(delta x) + df(x,y)/dy * delta y. I got (delta f)= z*lnx*(delta x) + (delta z)/x. When i plug in the numbers the units don't match up, i get cm*s + s/cm.

im really confused on how to find the answer can someone please help. thanks.

 

[Hootenanny]

delta f(x,y)=df(x,y)/dx *(delta x) + df(x,y)/dy * delta y]

That is not correct. In general:

$$\left(\Delta f(x,y)\right)^2 = \left(\frac{\partial f}{\partial x}\right)^2\Delta x^2 + \left(\frac{\partial f}{\partial y}\right)^2\Delta y^2$$

I got (delta f)= z*lnx*(delta x) + (delta z)/x

This is also in correct.

$$\frac{d}{dx}\left(\frac{1}{x}\right) \neq \ln|x|$$

 

[glasshut137]

oh jeez you're right thanks

 

[Hootenanny]

oh jeez you're right thanks

Take a note of my further comment, which was added after you replied.