(b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is formed by y = 5x, y = 14 – 2x and x = 7 for which х, у 2 0.

Q: 3) Consider the curve C in R³ given by: r(t) = (t + In t, t – In t, 4t'/²) con 1<t< 2 An expression…

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Q: Evaluate Se (5xy + x² + y²) dx + (x² - y)dy by using Green's theorem, where C is a closed curve that…

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: Use Green's theorem to evaluate , (5xy + x2 + y?) dx + (x²-y)dy where C is a closed curve that is…

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y-xy= 0 2y+5x+x-x'y² =…

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Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

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Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

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Q: The equation of the tangent plane to the surface x² z² at the point (-2, 1, 3) is Select one: + 2y.…

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Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: 4. Let f(z) = 1 23 1 - and find [ f(z) dz, where C a circle of radius 2 about the origin with…

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A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x-…

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Q: 19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).…

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Q: Find the equation for the Tangent Plane on the given surface coS ax – x²y + e*z+ yz = 4 Po(0, 1, 2)

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Q: 6. (a) Show that F = (3a²y+2, x3 + 3) is conservative. (b) Evaluate Sc(3x²y +2)dx + (x³ + 3)dy where…

A: According to the problem, we have

Q: 2. Find the work done by F in moving a particle once counterclockwise around the given curve C F =…

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Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: Since you have posted multiple questions according to company policy we are supposed to be answer…

Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: By using Green's theorem evaluate £ (Ary – y) dr + (** + 3ry) dy where C is a closed curve starting…

A: Green's theorem in a plane: If D is a region inclosed by a closed curve C then ∮C u dx+v dy=∫∫D…

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

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Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

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Q: 3. (a) Find the equation of the plane tangent to the surface given by f(x, y) = 2xª+2y^+7xy at the…

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Given:           x3−2y2+xy=0,     (1,1)

Q: 1. Compute (1/zy, 1/(z + y))- dr along the curve (t, t2). 1<ts4

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Q: Let C be any curve.

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Q: Use Green's theorem to evaluate S,(5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

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Q: Consider the curve C = C₁ U C₂ where C₁ is the line segment from (1,1,0) to (1,0,0) and C₂ is the…

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Q: Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses…

A: Here we will use greens theorem to find line integral of vector field For a vector field F→= Pi^+Qj^…

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Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C₂ is…

A: Given Data: The given curve is C=C1∪C2, where C1 is the line segment from 0,1,1 to 1,1,0 and C2 is…

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

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Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x2 + y2? (If an…

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: c) By using Green's theorem evaluate $ (4xy – y°) dx + (x³ + 3xy) dy where C is a closed curve…

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Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: According to the given information, it is required to use green’s theorem to evaluate the integral.