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Math Help - Determining whether a surface is smooth or piecewise smooth

  1. #1
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    Determining whether a surface is smooth or piecewise smooth

    Hello All,

    I would greatly appreciate any help for this problem for my Calc 3 class:

    Determine whether the given surface is smooth, piecewise smooth or neither.

    r(u,v)=<3u,u^2-2v,u^3+v^2>

    I took the derivative with respect to u, r(u):

    <3,2u,3u^2>

    And then with respect to v, r(v):

    <0,-2,2v>

    I then did the cross product, r(u) x r(v)

    And I got <2uv+6u^2, -6v, -6>

    Since this never equals 0, we can say that the surface is always smooth. Does that look correct?
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