1. Sketch the plane curve.
2. Find r'(t).
3. Sketch the position vector r(t) and the tangent vector r'(t) for the value t = 1.

Solution: a) We have and . Elimination of the parameter gives us , which is the equation of a parabola with vertex at ( 1, 0).

The position vector starts at the origin. As for the length of the vector, from the origin it moves to the right 2 and up 1.

The tangent vector r'(1) starts at the point (2,1) and moves 1 to the right and up 2.

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