Find the approximate value of $(401)^{\frac{1}{2}}$.

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

If the radius of a sphere is measured as $9 \ cm$ with an error of $0.03 \ cm$, then find the approximate error in calculating its surface area. (in $\pi \ cm^2$)

Consider the following statements:
$A$ is the relative error in the area of a square when the relative error in its side is $0.4$.
$B$ is the relative error in the volume of a sphere when the relative error in its radius is $0.3$.
$C$ is the relative error in the surface area of a closed cylinder whose height is equal to its radius,when the relative error in its height is $0.2$.
$D$ is the approximate error in $y = x^2 + x - 3$ when $x = 2$ and $\delta x = 0.1$.
The ascending order of the values of errors in these statements is:

What is an approximate value of $\sqrt{199}$ corrected to $4$ decimal places?

The approximate value of $\cot ^{-1}(1.001)$ is