If F = yi + (x - 2xz)j - xyk, evaluate the surface integral ff, (curl F) dS, where S is the surface of the sphere x² + y² + z² = a², z≥ 0. 2

Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

Q: calculate ∫Cy(x-z) ds, where C is the intersection of the surfaces x2+y2+z2=9 x+z=3

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Q: Let y= - Find the intersection of these surfaces, Calculate the GB of wrt lex order x>4>2)

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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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: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

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: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: olve the differential equation using Laplace transform. dy +4+4y=e-2t dt y (0) = 1 y'(0) = 2 d²y dt²

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Q: Let M⊂R ^ 3 be a surface and f be a diff.bilir function on this surface. Show that if Q is this…

A: Given: Let M⊂R3be a surface and let f be a differentiable function on this surface. If Q is a 1-1…

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: Problem 8. Fix a positive integer m. Given r € N, we consider the function fr : Zm → Zm defined by…

A: Here we have to fix a positive integer m such that: r∈ℕ, f:ℤm*→ℤm* defined by, fra=ar, for all a∈ℤ…

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

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Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

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