Differentials:
Find the differentials of the function.
- $T = \frac{v}{1+uvw}$
- $w = xye^{xy}$
More differentials:
If $z = x^2 -xy + 3y^2$ and $(x,y)$ changes from $(3,-1)$ to $(2.96,-0.95)$,
compare the values of $\Delta z$ and $dz$.
The dimensions of a closed rectangular box are measured as 80 cm, 60 cm, and 50 cm, respectively,
with possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error
in calculating the surface area of the box.
Even more differentials:
Four positive numbers, each less than 50, are rounded to the first decimal place and then multiplied together.
Use differentials to estimate the maximum possible error in the computed product that might result from the rounding.