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4) Consider the polar curve r=e2theta a) Find the parametric equations x = f(θ), y =...

4)

Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y = g(θ) for this curve.

b) Find the slope of the line tangent to this curve when θ=π.

6)

a)Suppose r(t) = < cos(3t), sin(3t),4t >.

Find the equation of the tangent line to r(t) at the point (-1, 0, 4pi).

b) Find a vector orthogonal to the plane through the points P (1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the area of the triangle PQR.

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