If $y=2x^3-2x^2+3x-5$, then for $x=2$ and $\Delta x=0.1$, the value of $\Delta y$ is:

The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3 \%$ is (in $x^{3} \text{ m}^{3}$)

If the percentage error in the radius of a circle is $3\%$,then the percentage error in its area is:

Using differentials,find the approximate value of $\left(\frac{17}{81}\right)^{\frac{1}{4}}$.

The semi-vertical angle of a right circular cone is $45^{\circ}$. If the radius of the base of the cone is measured as $14 \text{ cm}$ with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \text{ cm}$,then the approximate error in measuring its total surface area is (in $\text{sq. cm}$):

Using differentials,find the approximate value of $(33)^{-\frac{1}{5}}$.