A torus of radius 2 (and cross-sectional radius 1) can be represented parametrically by the function r : D → R³: r(0,0) = ((2 + cos ) cos 0, (2 + cos ) sin 0, sin o) where D is the rectangle given by 0 ≤0 ≤ 2π, 0≤ ≤ 2T. The surface area of the torus is

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

A:

Q: Show that the parametric equations x =a sin u cos v, y =b sin u sin v z=c cos u 0<u <pi  0 v…

A: Here,

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Describe the projections of the circle r(t) =〈sin t, 0, 4 + cost〉onto the coordinate planes.

A:

Q: 8.) Consider the contour C in the complex plane consisting of the portion from z = 1 to z = 2+ i. of…

A: A.Now, let's find an antiderivative of z^{2} with respect to z. We have \frac{1}{3}z^{3}+C, where C…