5. Given the curve x(u) = sin(u) + 2 cos(2u) and y(u) = cos(u) + 2 sin(2u). The parameter u does not represent time. (a) Find the unit tangent vector T and the unit normal vector N when u = 0 (b) Sketch the sectors on thes Purves (c) Compute the curvature when u = 0. (d) Suppose the curve represents a new slot car race-track, find the exact location where the normal acceleration of the car will be the largest if one keeps the car at constant speed.

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