Question

if the measured values of two quantities are A+-deltaA and B+-deltaB,delta and deltaB being the mean absolute errors .what is the maximum possible error in A+-B? show that if z= A/B
deltaZ/Z=deltaA/A+deltaB/B​

Answer 1

Answer:

Explanation:

Here is your answer

Answer 2

Answer:

L.H.S = R.H.S

Explanation:

According to this question

We have been given that

Z = $\frac{A}{B}$

So, we can add both side maximum possible error

$Z \pm \delta Z$ = $\frac{A \pm \delta A} {B \pm \delta B}$

$Z \pm \delta Z$ = $(A \pm \delta A)\times (B \pm \delta B)^{-1}$

$Z[1 \pm (\frac{\delta Z}{Z})]$ = $A[1 \pm (\frac{\delta A}{A}]\times B^{-1}[(1 \pm \frac{\delta B}{B})^{-1}]$

$Z[1 \pm (\frac{\delta Z}{Z})]$ = $\frac{A}{B}[1 \pm (\frac{\delta A}{A}]\times [(1 \pm \frac{\delta B}{B})^{-1}]$

From question Z = $\frac{A}{B}$

then, $[1 \pm (\frac{\delta Z}{Z})]$ = $[1 \pm (\frac{\delta A}{A}]\times [(1 \pm \frac{\delta B}{B})^{-1}]$

$\pm 1 \pm (\frac{\delta Z}{Z})$ = $\pm 1 \pm \frac{\delta A}{A}\ \pm \frac{\delta B}{B}\ \pm \frac{\delta A\times \delta B}{AB}$

$\pm (\frac{\delta Z}{Z})$ = $\pm \frac{\delta A}{A}\ \pm \frac{\delta B}{B}\ \pm \frac{\delta A\times \delta B}{AB}$

$\frac{\delta A\times \delta B}{AB}$ value is very negligible so we can remove that.

$\pm (\frac{\delta Z}{Z})$ = $\pm \frac{\delta A}{A}\ \pm \frac{\delta B}{B}$

Hence, proved