ate 3 and y = 0. S S SV E 4y² dv where E is the solid below 2 = -37²-3y² and above 2=-12
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- Use Green's Theorem to evaluate∮tan^-1(y)dx-(xy^)/(1+y^2) dy where C is the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1) and oriented counterclockwise. A. -1 B. 2 C. 1 D. -2C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0, −10), directed counter-clockwise. Evaluate integralC (3y/(x^2+y^2) dx − 3x/(x^ 2 + y^2) dy)Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x and y axes and the line y=-x+1? Thank you
- Find the point on the curve of intersection of the paraboloid x² + y2 + 2z = 4 and the plane x - y + 2z = 0 that is closest to the origin. (1,-1,1) (1,1,1) (1,1,-1) (-1,1,1)Find a point on the ellipsoid x2 + 3y2 + z2 = 8 where the tangent plane is perpendicular to the line with parametric equations X = 1 - 4t, y = 5 + 6t, and z = 2 - 2t. |) (smaller x-value) |) (larger x-value) (х, у, 2) 3 ( (х, у, 2) %3D (|Find the centroid of the triangle with vertices (−2, −2), (4, 1) and (4, 4).