Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 - y? that lies above the square 0 < a < 5, 0

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the…

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Q: Show G(r,0) = (rcose, rsine, 1-r^2) parametrizes the paraboloid z=1-x^2-y^2. Afterwhich, descrbie…

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Q: Let S be the paraboloid y = x^2 + z^2. Find a parametric representation for S and its tangent plane…

A: The given data is: Let S be the paraboloid y=x2+z2 Find a parametric representation for S and its…

Q: Sketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.

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Q: Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.

A: Given: The equation is x=4-z2. To sketch: The given equation in three-dimensional space.

Q: How can I parametrize this 3D shape with two variables? x ≥ 0, 0 ≤ y ≤ x, x^2 + y^2 ≤ z ≤…

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Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: Evaluate SdV where G is enclosed by the paraboloids z = G z = 4 x² - y². Answer: 2π 3x² + 3y² and

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Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: Use hyperbolic functions to parametrize the intersection of the surfaces x' - y 49 and z= (Use…

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Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: Q3] (A) Verify Stokes' theorem where Ã= (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z =…

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Q: Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the cone z = x² +…

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Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: The tangent plane to the surface 2x² + 3y² = 5z² at (1, 1, 1) has an equation ax +by+cz = d.What is…

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Q: Let S be the surface given by the first octant part of the paraboloid z=4-x^2-y^2. Find the area of…

A: We need to determine the surface area of the surface bounded by the paraboloid: z=4-x2-y2 in the…

Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Q: Q1.6 Find the point on the surface given by the equation x^2 + 5y^2 + 10z^2 = 18016 that has a…

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: '99 '37 37 XCOS Z Evaluate dzdydx. and the sphere

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