The function
r(u,v)=x(u,v)Subscript[e, 1]+y(u,v)Subscript[e, 2]+[2x(u,v)^2-y(u,v)^2]Subscript[e, 3],
x(u,v)=2u cos v, y(u,v)=3u sin v, 0<=u<=1/2, 0<=v<=2\[Pi]
parametrizes the part of the hyperbolic paraboloid z=2x^2-y^2 with (x,y) restricted to the ellipse x^2/4+y^2/9<=1/4.
1.A. Use formula (1) and Mathematica's built-in command Integrate[] to calculate the surface area of [CapitalSigma]. 1.B. Use the module SurfaceAreaApproximation[] to approximate the surface area of [CapitalSigma] using 36 parallelograms. 1.C. Use the module SurfaceAreaApproximation[] to approximate the surface area of [CapitalSigma] to within 0.5. How many parallelograms did you use?
The function
r(u,v)=x(u,v)Subscript[e, 1]+y(u,v)Subscript[e, 2]+2exp[-2 x(u,v)^2-2y(u,v)^2]Subscript[e, 3],
x(u,v)=u cos v, y(u,v)=u sin v, 0<=u<=1, 0<=v<=2\[Pi]
parametrizes the part of the graph of the function z=2e^(-2 x^2-2y^2) with (x,y) restricted to the circle x^2+y^2<=1.
2.A. Use formula (1) and Mathematica's built-in command Integrate[] to calculate the surface area of [CapitalSigma]. 2.B. Use the module SurfaceAreaApproximation[] to approximate the surface area of [CapitalSigma] using 36 parallelograms. 2.C. Use the module SurfaceAreaApproximation[] to approximate the surface area of [CapitalSigma] to within 0.5. How many parallelograms did you use?
I am confused as to what values to use in this module for r and i
P = Table[ Point[r[-1 + (i 2)/5, -(\[Pi]/2) + (j \[Pi])/5]], {i, 0, 5}, {j, 0,5}];
B = Graphics3D[{AbsolutePointSize[7], RGBColor[0, 0, 0], P}, Axes -> False, Boxed -> False];SS = Show[A, B]
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