Consider the limaçon y(t) = ((1+3 cos t) cost, (1 +3 cost) sin t). (i) Compute A(Y) = f(xy-yx)dt, (ii) Determine the osculating circle C at (4,0), (iii) Show that y lies entirely inside C,

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A: Given that                Then            At  , we need to find the value of .

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A: Given that, r→t=4 cos 5t,  4 sin5t,  5t  at the point   t=0

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A: given that                                          r→(t)=4cos(2t), 4sin(2t), 2t at t=0…

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A: The plot of the curve for t within 0 to 2pi is shown in figure below.

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A:

Q: Find T', N and B for the curve 7 (t) = (2 cos(2t), 2 sin(2t), 3t) at the point t = 0 Give your…

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A: Given surface is,This equation represents a surface in three-dimensional space.To find the: