(Steps Shown) Here's a plot of the surface z=3-fracy^24-x/2 over the region R in the xy -plane consisting of all points (x, y, 0) with (x, y) inside the 2D
Question: Here's a plot of the surface
\[z=3-\frac{y^{2}}{4}-\frac{x}{2}\]over the region \(\mathrm{R}\) in the \(\mathrm{xy}\) -plane consisting of all points \((\mathrm{x}, \mathrm{y}, 0)\) with \((x, y)\) inside the 2D circle
\[x^{2}+y^{2}=4\]with a plot of \(R\).
Come up with a counterclockwise parameterization \((\mathrm{x}(\mathrm{t}), \mathrm{y}(\mathrm{t}))\) of the circle
\[x^{2}+y^{2}=4\]Use your parameterization and the Gauss-Green formula to measure by hand calculation the volume off the solid whose top skin is the plotted surface and whose bottom skin is the rectangle \(\mathrm{R}\).
Deliverable: Word Document 
![[Step-by-Step] Go with f(x)= sin (2 x)](/images/solutions/MC-solution-library-37608.jpg "[Step-by-Step] Go with f(x)= sin (2 x) Give a clean formula for the")
[Step-by-Step] Go with f(x)= sin (2 x) Give a clean formula for the
![[Solution Library] Go with f(x, y)=2 e^-x^2](/images/solutions/MC-solution-library-37609.jpg "[Solution Library] Go with f(x, y)=2 e^-x^2 cos (y) Give a clean")
[Solution Library] Go with f(x, y)=2 e^-x^2 cos (y) Give a clean
(Step-by-Step) Write down the Gauss-Green formula and say how to use
(See Solution) Here is a 2 D region R with bottom boundary curve low;(x)=x(x-1)
![[All Steps] Here is a 2D region](/images/solutions/MC-solution-library-37612.jpg "[All Steps] Here is a 2D region R whose left boundary is the curve")
[All Steps] Here is a 2D region R whose left boundary is the curve
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