6. Consider the path given by r(t) = (cost, cost sint, sin² t), 0 ≤ t ≤ 2π. (a) Show that the path is a parameterization of a curve that lies on the unit sphere. (b) Find a parametrization of the line tangent to the curve when t = π/2. (c) Show that the path is a parameterization of a curve that lies on the parabolic cylinder z = 1-x².

Q: ) Find symmetric equations for the tangent line to the graph of f(r, y) = at (1, 2, 2) in the plane…

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Q: 3) Find the radius of curvature for the parametric curve e-t cost , y = e-t sin t.

A: Given parametric curve is x=e-tcost, y=e-tsint. We know that the Radius of curvature of a parametric…

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Q: Pls help

A: We have to find the horizontal asymptote.

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A: Please check step 2 for solution.

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Q: The cycloid generated by the unit circle has parametrizationr(t) = (t − sin t, 1 − cost)(a) Find the…

A: Given :           The parametrization of the cycloid is r(t) = (t - sin t, 1 - cos t).

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Q: Yk = B1(k) – 1/½B2(k) + /½B4(k) + A1,

A: We have given the particular solution by equation (2.63). yk=k-1-kk-12+k-12k22      from (2.63)

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Q: a) y = x' – 9x?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: 4. Consider the parametric curve x = cost, y = sin cost, te [-T, π]. (a) Show that (0,0) is a point…

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A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…