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The cycloid is the curve traced by a point on the wheel rolling along the x-axis. Its parametric equations are x = t - sin(t/R)

The cycloid is the curve traced by a point on the wheel rolling along the x-axis. Its parametric equations are

x = t - sin(t/R)

y = R(1 - cos(t/R))

(a) Find the curvature of the cycloid as a function of t.

(b) What happens with the curvature as t --> 0?

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