Using differentials,find the approximate value of $\sqrt{0.082}$. Let $f(x) = \sqrt{x}$.

There is a possible error of $0.02 \ cm$ in measuring the base diameter of a right circular cone as $14 \ cm$. If the semi-vertical angle of the cone is $45^{\circ}$,then the approximate error in its volume is (in $cm^3$)

If $1^{\circ} = 0.0175 \text{ radians}$,then the approximate value of $\sec 58^{\circ}$ is

Given $f(x) = x^3 - 4x$,if $x$ changes from $2$ to $1.99$,then the approximate change in the value of $f(x)$ is

Find the approximate value of $(255)^{\frac{1}{4}}$.

$A$ point on the hypotenuse of a triangle is at distances $a$ and $b$ from the sides of the triangle. Show that the minimum length of the hypotenuse is $(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}$.