Estimate the change in the volume of a cylinder when its radius changes from $r=2\text{ m}$ to $r=2.02\text{ m}$, given the height $h=5\text{ m}$. Note: $V\left(r\right)=\pi r^{2}h$.

Provide the differential expression $dy=f^{\prime }\left(x\right)dx$ for the following function:

$f\left(x\right)=2{\sin }^2\left(2x\right)$

Provide the differential expression $dy=g^{\prime }\left(x\right)dx$ for the following function:

$g\left(x\right)=3-b\cos \left(2x\right)$, where $b$ is a constant

Provide the differential expression $dy=h^{\prime }\left(x\right)dx$ for the following function:

$h\left(x\right)=\frac{x+8}{8-x}$