Let the surface S be part of the cone z2 = x2 + y2 which is inside the cylinder x2 + y2 = 2y, outside cylinder x2 + y2 = 1 and above the xy plane.

Q: Find the equation of the surface of revolution generated by rotating the given curve about the…

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Q: A surface is defined by coordinate or parametric functions of more than two variables. Select one:…

A: A surface is defined by coordinate or parametric functions of more than two variables.

Q: Sketch the graph of the parametric surface. x= sinh u, y=v, z=2cosh u.

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Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: (a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**)…

A: Surface integral of a function f(x,y,z) on a parametric surface r(u,v) in the region D  ∫∫Dfx(u,v) ,…

Q: Please make sure its right. calc 3 Find a parametric representation for the part of the plane z = x…

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Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Transform (0, y) from rectangular into polar form (here y is any negative number).

A: We have convert rectangular coordinates (0 , y) into polar coordinates: Where y is negative number-

Q: 1) Let S be the surface of the cylinder r+y = 4 with y >0 and -15z<1. Find a parametric equation…

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Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

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Q: Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2…

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Q: Find the distance on the xy plane between the two points, given below as polar coordinates (7,…

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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: The curve (x-)*+Cy +1)*= 4, x 7,1 is given. First draw it in the Cartesian plore and then transtorm…

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…

A: The equation of the surface of revolution given is as follows:…