In Exercises 1–12, sketch the graph described by the following cylin- drical coordinates in three-dimensional space. 1. r = 2 п 2. 0 = 3. z = -1 4. z = r 5. r = 0 6. z = r sin 0 7. r² + z? = 4 8. 1

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A: Given Finding the derivative with respect to t:

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A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

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A: A strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the…

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A: We know that Green's theorem

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A: Introduction: The parametrization is a very significant part that is related to vector calculus.…

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A: The answer is given below thank you for the question upvote is really appreciable

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Q: Consider the cune C: (x-8)+ 4-7) When parametneing C, A tungent veotoar is i O a) r (0) = (8 +3…

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Q: Calculate the circulation of A = p cos ap + z sin o az around the edge L of the wedge defined by 0 ≤…

A: Yes , we can solve using stokes theorem. Note that all the cases z = 0

Q: Find a piecewise smooth parametrization of the path C. 0 st<1 (ti+tj r(t) = %3D 1<t<2 (1, 1) y=x

A: Given rt=ti + tj                             0≤t≤1                                       1≤t≤2

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A: Here we compare r as its basic equation to prove this.

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A: Given: r(t)=8cost+8sint+tk    [0,pi/2]

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Q: xy = 4

A: Solution

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A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

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Q: To illustrate that the tength of a smooth space curve does not depend on the parameterization used…

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Q: 2. Consider the three-dimensional system r=r(1-r) e' = 1 2 = -2. Hand written plz Compute the…

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Q: Let Ci be the rectangle with vertices (0,0), (2,0), (0,1), and (2,1) oriented counterclockwise, and…

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A: parametric equations for a cylinder of radius 3 x^2+y^2+z^2=r^2 Where r=3