The velocity field of a fluid (in meters per second) is

\[
\mathbf{F}=(3 y-4) \mathbf{i}+e^{-y(z+1)} \mathbf{j}+\left(x^{2}+y^{2}ight) \mathbf{k}
\]

(a) Estimate the flow rate (in cubic meters per second) through a small surface \(\mathcal{S}\) around the origin if \(\mathcal{S}\) encloses a region of volume \(0.01 \mathrm{~m}^{3}\).

(b) Estimate the circulation of \(\mathbf{F}\) about a circle in the \(x y\)-plane of radius \(r=0.1 \mathrm{~m}\) centered at the origin (oriented counterclockwise when viewed from above).

(c) Estimate the circulation of \(\mathbf{F}\) about a circle in the \(y z\)-plane of radius \(r=0.1 \mathrm{~m}\) centered at the origin (oriented counterclockwise when viewed from the positive \(x\)-axis).