Find the equation of the tangent plane of the following surface patches at the indicated points: (a) σ(u,v) = (u,v,u2 + v2), P = (1,√2,3).
(b) σ(r,θ) = (rcosθ,rsinθ,2θ), P =(√3,1, π 3).
(a) Show that the circular cylinder S = {(x,y,z) ∈R^3 : y^2+z^2 = 1}can be covered by a single regular surface patch, and hence is a surface.
(b) Draw a picture describing this surface patch.
(a) Show that the circular cylinder S = {(x,y,z) ∈R3 : y2+z2 = 1} can be covered by a single regular surface patch, and hence is a surface.
(b) Draw a picture describing this surface patch.
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