Just as you describe curves in the plane parametrically with a pair of equations x = (t),

Just as you describe curves in the plane parametrically with a pair of equations x = ƒ(t), y = g(t) defined on some parameter interval I, you can sometimes describe surfaces in space with a triple of equations x = ƒ(u, ν), y = g(u, ν), z = h(u, ν) defined on some parameter rectangle a ≤ u ≤ b, c ≤ ν ≤ d. Many computer algebra systems permit you to plot such surfaces in parametric mode. Use a CAS to plot the surfaces. Also plot several level curves in the xy-plane.

Transcribed Image Text:

Xu Cos U, 0 ≤ V≤ 2TT y = u sin v, z = v, 0≤u ≤ 2,