Evaluate [(yzi + y° i+ xzk)•d$ where S is the boundary of a cuboid defined by -1sxs1, -1sys1 and 0szs2.

Q: Find the integral surface of the linear PDE xp - yq = z which contains the circle x² + y? = 1, z=1.

A: From Lagrange method

Q: 5. Let C be the circle x +y} =4_which is positively oriented. Let C, be the upper half-circle C1 =…

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Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: Sketch the surfaces PARABOLOIDS AND CONES z = 8 - x2 - y2

A: Consider the equation of the surface, z = 8 - x2 - y2

Q: Let a, b be positive real number, F = (esinx + y) i+ (3x – 4(tan y) )j, and C be the boundary of the…

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Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

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Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

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Q: Consider the region R bounded by the parabolas y = and y = r - 3.r, as depicted in the graph below.

A: Since you have posted multiple questions but according to guidelines, we will solve the first…

Q: et the affine map A : R? → R² be defined by A(x, y) (3x + 4, 2y – 3). Show that the image of a unit…

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Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

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Q: Which of the following correctly represents the plane region in the first quadrant bounded by the…

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Q: The distance between the centers of the following two spheres: x²+10x+y²+14y+z²=-73,…

A: Given that: x2+10x+y2+14y+z2=-73      .......(1)2x2-4x+2y2+2z2+8z=-5     ........(2)

Q: show. that theAine in.which.the planes.X+.2y-22=-5 nod5X-2y.z=.0...jntersec.is..pavalle.to.theine.…

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Q: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

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Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Determine the projection of the following surface on the xz plane. (xz trace) 4x – + = 0

A: Given equation of surface is 4x-y24+z28=0

Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

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Q: use the mthod of trig substitution to prove the area of the ellipse " {(x^2)/(a^2)}+{(y^2)/(b^2)} =…

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Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Which of the following point is the closest point on the sphere z² + y² + z² = 4 from the point…

A: Given Equation of Sphere X2+y2+z2=4 And point (3, 1, -1)

Q: Let C denote the triangle with vertices at (0, 0), (0, 1) and (2, 1), oriented positively. Then f(x²…

A: We have to apply the green's theorem here.

Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Sketch the solid described by the given inequalities. 3sps 4, os ps a/3, 0S0SR 1.5 21.0 0.5 00…

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Q: Use the Green's theorem to calulate So (3x²y – xy? – 3.x²y²) dx + (x³ – 2.x³y+ x²y) dy, where C is…

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Q: Let C be the intersection curve of the parabolic cylinder √2x2 = 2y and the surface 3z =√2xy. Find…

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Q: 3.4.8 Show that the sphere x² + y² + z² = 1, z ≥ 0. JJ,z²dS=, where S is the surface of

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Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: Let E be the region in the plane between the two ellipses 4x² +9y? = 1 and 4x2 + 9y2 = 4. Evaluate…

A: Given that two ellipse 4x2+9y2=1 and 4x2+9y2=4 Ans given E be the region in the plane between these…

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: D is the region enclosed by the parabolas z = y²-9 and 2 - y² +9.

A: Let, I=∫∫Dx+y+2dA x=y2-9 and x=-y2+9 Power rule for the integration: ∫xndx=xn+1n+1+C ∫cdx=c∫x0dx=cx

Q: If o is the sphere of radius 2 centered at the origin, then (x² + y² + z³) d$ =

A: Given the sphere

Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: (a) Find max, min or saddle points for the surface Z= x* - 3xy + 5x

A: We have to find first and second order partial derivatives.

Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: Evaluate |(y zi+y°i+xzk)•d$ where S is the boundary of a cuboid defined by S -15x<1, -1<ys1 and…

A: The given integral: S=∬s(y2zi→+y3j→+xzk→) dS Where S is the boundary of cuboid defined by -1≤x≤1,…

Q: T 1) Reflect quadrilateral ABCD across the y-ar reflection on the coordinate plane to the right. new…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let C be the curve of intersection of the parabolic cylinder x? = 2y, and the surface 3z = xy. Find…

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Q: Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of…

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Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…