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In: Math

Let r : R->R3 be a path with constant speed, satisfying r"(t) = (4 sin(2t))i +...

Let r : R->R3 be a path with constant speed, satisfying

r"(t) = (4 sin(2t))i + (-4 cos t)j + (4 cos(2t))k for all t belongs to R:

Find the curvature w.r.t. t of r. (Hint: cos(2t), sin(2t), and cos(t) are linearly independent. i.e. if c1cos(2t) + c2sin(2t)+
c3cos(t) = 0 for all t belongs to R, then c1 = c2 = c3 = 0.)

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