1. Give a parametrization of the line segment connecting the points $(1,2,3)$ and $(2,-3,5)$.
  2. Give a parametrization of the ellipse $\ds\frac{x^2}{16}+\frac{(y-3)^2}{25}=1$.
  3. Give a parametrization of the function $y=x^3-3x+7$ for $x\in [-2,3] $.
  4. Give a parametrization of the surface $z=x^2+y^2$.
    • Using rectangular coordinates.
    • Using polar coordinates.
    • Give bounds for the portion of this surface below $z=4$, for each parametrization above.

Problem Set
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