a) Parameterize the curve of intersection of the surfaces so that the direction is counterclockwise when viewed from above: z = xy x² + y² = 1 b) Compute the surface area of the portion of the surface z = cylinder x² + y² = 1. xy that lies inside the

Q: 1= {cx,y,?): + = 1, 2= 0} %3D А) b?(а — х)? 3D а? (у? + 2?) в) ь? (а + х)? %3 а?(у? — z') С) 6? (а?…

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

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Q: Find the area of the surface cut out from the bottom of the paraboloid z = x² + y² by the plane z =…

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Q: Explain briefly how Vø relates to surfaces of constant o(x, y, x). Hence, use Vø to find points in…

A: For the surface of constants ϕx,y,z=k, the gradient vector ∇ϕx0,y0,z0 is orthogonal to the level…

Q: Find the angle between the surfaces x² + y² + z² = 41 and z = x² + y²-11 at the point (4, 0, 5):

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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: Find the equation of the surface of revolution that is generated by rotating the straight line y = x…

A: The surface of revolution that is generated by rotating x=f(y) around the y-axis is x2+z2=f(y)2 so…

Q: Find the cylindrical equation for the surface whose rectangular equation is x² + y² - 2y = 0.

A: Given rectangular equation is,We have to find cylindrical equation for the surface.

Q: Find the surface area of the part of the paraboloid z=2x² +2y² that lies under the plane 2=16.

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Q: Since it is known that x2 + y? = c², write the expression below in terms of c2 -2(x8+ y®) + 28(x6+…

A: -2(x⁸+y⁸) = -2{(x⁴+y⁴)² - 2x⁴y⁴} = -2{(x²+y²)² - 2x²y²}² + 4x⁴y⁴ = -2(c⁴ - 2x²y²)² + 4x⁴y⁴ = -2(c⁸ -…

Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: On solving this we will get

Q: Sketch the portion of the surface that lies in the first octant: x = z.

A: Sketch the portion of the surface that lies in the first octant: x = z.

Q: Find the surface area of that part of the plane 2x + 3y + z = 3 that lies inside the elliptic…

A: Given: The plane is: 2x+3y+z=3. The elliptic cylinder is: x225+y29=1. To Find: The surface area of…

Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

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Q: Write the differential equation (unlimited, limited, or logistic) that applies to the situation…

A: Given that, the initial cases are N0=14. "It is known that, the formula for the exponential growth…

Q: arameterize the intersection of the plane x = 1 and the surface z = x2 - 2x2y + y2.

A: To parameterize the intersection of the plane x = 1 and the surfacez=x2−2x2y+y2, we can set x = 1 in…

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: lim Sin(1-Cost) 1- Cast ·

A: limt→0 sin1-cost1-cost