# Thread: Using differentials to estimate a maximum error

1. ## Using differentials to estimate a maximum error

Four positive numbers lesser than 50 each are rounded to the first decimal and then multiplied between themselves. Use differentials to estimate the maximum possible error of the product.
My attempt : Let $\displaystyle x$, $\displaystyle y$ and $\displaystyle z$ be the 3 numbers.
We have $\displaystyle (x+\Delta x)(y+\Delta y)(z+\Delta z)=0.1(zx+zy+xy)+0.01(z+x+y)+0.001$.
Note that I considered $\displaystyle \Delta x = \Delta y = \Delta z =0.1$.
However I don't see how I can use differentials. I don't see any way to involve them. So I didn't solve the problem...
Do you have any idea?

2. If P is the product and x,y,z are numbers, then

$\displaystyle P=xyz$

hence, we have,
$\displaystyle dP=yzdx + xzdy + xydz$

For maximum possible error, dx, dy and dz are maximum.

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You have used

$\displaystyle \Delta x = \Delta y = \Delta z =0.1$

It cant be >0.5

3. Ok you've done $\displaystyle dP=\frac{\partial P}{\partial x}+\frac{\partial P}{\partial y}+\frac{\partial P}{\partial z}$.
But then you wrote
For maximum possible error, dx, dy and dz are maximum.
but these are differentials. I don't see how $\displaystyle dx$, $\displaystyle dy$ and $\displaystyle dz$ can have a maximum value if any numerical given value.
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You have used

It cant be >0.5
Ok, so I'm correct then?