Draw each curve or surface given below.

  1. $\vec r(t) = (3\cos t,3\sin t)$ for $0\leq t\leq 2\pi$.
  2. $\vec r(u,v) = (3\cos u,3\sin u,v)$ for $0\leq u\leq 2\pi$ and $0\leq v\leq 5$.
  3. $\vec r(u,v) = (4\cos u,v, 3\sin u)$ for $0\leq u\leq \pi$ and $0\leq v\leq 7$.
  4. $\vec r(t) = (3\cos t,3\sin t,4t)$ for $0\leq t\leq 6\pi$.
  5. $\vec r(u,v) = (u\cos v,u\sin v,v)$ for $0\leq v\leq 6\pi$ and $2\leq u\leq 4$.
  6. $\vec r(t) = (0,t,9-t^2)$ for $0\leq t\leq 3$.
  7. $\vec r(u,v) = (u\cos v,u\sin v,9-u^2)$ for $0\leq v\leq 2\pi$ and $0\leq u\leq 3$.

Problem Set
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