Find the approximate value of $(1.999)^{5}$.

If the semi-vertical angle of a cone is $45^{\circ}$ and its height is $20.025 \text{ cm}$, then the approximate value of its curved surface area (in $\text{sq. cm}$) is

If $1^{\circ} = \alpha$ radians,then the approximate value of $\cos(60^{\circ} 1^{\prime})$ is

Find the approximate value of $\sqrt{0.6}$ using differentials.

The radius of a cone of height $9 \text{ units}$ is changed from $2 \text{ units}$ to $2.12 \text{ units}$. The exact change and approximate change in the volume of the cone are respectively:

If $y = (1 + \alpha + \alpha^2 + \ldots) e^{nx}$,where $\alpha$ and $n$ are constants,then the relative error in $y$ is