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Letr(t)=(4t2+1)i+2tjfor−2≤t≤2. (a) (10 pts) Draw a sketch of the curve C determined by r(t). (b) (5...

Letr(t)=(4t2+1)i+2tjfor−2≤t≤2.

  1. (a) (10 pts) Draw a sketch of the curve C determined by r(t).

  2. (b) (5 pts) Plot r(0) and label its endpoint P.

  3. (c) (10 pts) Plot the vector tangent to C at P .

  4. (d) (10 pts) Find the equation of the line tangent to C at P (you may give this parametrically

    or not).

  5. (e) (5 pts) Find the curvature K at P .

  6. (f) (5 pts) Find the radius of curvature ρ at P.

  7. (g) (5 pts) Sketch the circle of curvature (the circle of best fit) at P.

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