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  3. given the parametrized curve r(u) = a cos u(1 ? co

Given the parametrized curve r(u) = a cos u(1 ? cos u)ˆi + a sin u(1...

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Advance Math

Given the parametrized curve r(u) = a cos u(1 ? cos u)ˆi + a sinu(1 ? cos u)ˆj, u ? [0, 2? [ , (with a being a constant)

i) Sketch the curve (e.g. by constructing a table of values orsome other method)

ii) Find the tangent vector r 0 (u). What is the tangent vectorat u = 0? And at u = 2?? Explain your result.

iii) Is the curve regularly parametrized? Motivate your answerusing the definition.

iv) Compute the length of the arc corresponding to the interval[0, ?/2].

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Matlab code for plotting parametric curveclear allclose allfunction for rurxua acosu1cosuryua asinu1cosulet us consider a5ttlinspace02pi25printing rx    See Answer
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