<s>[INST] Approximate $\sqrt{(1.02)^3+(1.97)^3}$ using differential So $$\sqrt{(1.02)^3+(1.97)^3}=\sqrt{(1+0.02)^3+(2-0.03)^3}$$
So the differential will be $$\sqrt{1^3+2^3}+\frac{3(1)^2}{2\sqrt{1^3+2^3}}\Delta x+\frac{3(2)^2}{2\sqrt{1^3+2^3}}\Delta y=3+\frac{1}{2}\Delta x+2\Delta y$$
is $\Delta x=0.02 \text{ and } \Delta y=-0.03$ or $\Delta x=(0.02)^3 \text{ and } \Delta y=(-0.03)^3$?
 [/INST] For  $$\sqrt{(1.02)^3+(1.97)^3}=\sqrt{(1+0.02)^3+(2-0.03)^3}$$
The correct choice is  $$\Delta x=0.02 \text{ and } \Delta y=-0.03$$
Note that you have changed your $x$ from $1$ to $1.02$, which means your change in $x$ is 
 $ \Delta x=0.02$
Similarly for change in $y$ from $2$ to $1.97$ we have  $\Delta y=-0.03$
</s>