Consider the vector field F = < x²y°, x*y² > F . dī along the curve C: F(t) = 7 cos(t)i + 7 sin(t)3, 0

Q: What is the (numerical) value of the 3-form field (x² + y + z?) dx A dy A dz on the ordered triple…

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Q: Consider the vector field F Evaluate F · dī along the curve C: F(t) = t?i + t°j, 0<t<1

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Q: Consider the vector field F(x, y) = (3y² – 2xy, 6ry – x²). (a) Show that F is conservative. (b) Find…

A: According to question, Given vector field, F→x, y = 3y2 -2xy, 6xy-x2

Q: Consider the vector field F (2x + 5y, 5x + 7y) Is this vector field Conservative? Conservative If…

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Q: xi + yj x2 + y2 F(x, y) = k-

A: Topic- vector integration

Q: Evaluate the line integral F dr of the vector field F (x, y) = (x - y)i + (x + y) j C; r (1) = 4 cos…

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Q: Consider the vector field F Evaluate F · dr along the curve C: C 7(t) = 6 cos(t)i + 6 sin(t)j, 0…

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Q: Find an expression for the vector field F = ⟨x - y, y - x⟩ (in terms of t) along the unit circle…

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Q: Evaluate F. dr for the vector field F(x,y) = xy²i+ x²yj where C is given by r(t) = cos (t)i + 2 sin…

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Q: Consider the vector field F So Evaluate F · dī along the curve C: C F(t) = 4 cos(t)i + 4 sin(t)j, 0…

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Q: Consider the vector field F = (7x + 3y, 3x + 2y) Is this vector field Conservative? ( Conservative…

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Q: Consider the vector field F = Evaluate F · dr along the curve C: T(t) = t²i + t³j, 0<t< 1

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Q: Evaluate the line integral of the vector field F(x, y, z) = (x²y³, e™y+z, x+ z²) around the circle…

A: Solution is as below

Q: Let a vector field F(х,у) 3sinx 1 + ху ј be given. What is the integral representing the work done…

A: Workdone by force along the path is integration (f.dl) Where f is force and dl is distance vector…

Q: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

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Q: Consider the vector-field F(x, y) = y²i-xj, and let C be the arc of the parabola y = k – x² from the…

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Q: Consider the vector field F and the curve C below. F(x, y) = (7 + 2xy²)i + 2x²yj, %3D 4) C is the…

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Q: Consider the force field F = (y, –2x² y) in R². Suppose that an object moves along the parametrized…

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Q: Consider the force field F = (ev – e2" , (x + })ev) and the curve C = C¡U C2 where Cı is the line…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the work done by the field F(x,y, z) = (6z, 12x, y?) along the curve r(t) (cos(t), sin(t),…

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Q: Find the curl of the vector field F = (4x sin(y), 7y cos(x)). curl F - Dretieur

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Q: Consider the vector field F and the curve C below. F(x, y) = (7 + 2xy²)i + 2x²yj, %3D C is the arc…

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Q: Find the curl of the vector field F = (6y cos(x), 7x sin(y)) curl F =

A: If  F=f1x,y, f2x,y   thenCurl F=0,0,∂f2∂x-∂f1∂y

Q: Consider the line integral (Image 1) , where C is defined by the vector function: r (t) = - t2i +…

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Q: Integrate the vector field h(x,y) = y^2i + (2xy-e^2y)j over the circular arc C parametrized by r(t)…

A: The answer is given by using the formula of line integral

Q: Consider the vector field F and the curve C below. F(x, y) = (3 + 4xy2)i + 4x²yj, C is the arc of…

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Q: Consider the vector field F = (r'y*, z*y") Is this vector field Conservative? Select an answer v If…

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Q: Ex: Find the work done by the vector field F = (y-x²)i + (z - y²)j + (x-z²2)k Over the curve r(t) =…

A: Given: F=y-x2i+z-y2j+x-z2krt=ti+t2j+t3k

Q: Consider the vector field F Evaluate |F. dī along the curve C: 7(t) = tỉ +t°j, 0 <t < 2

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Q: Is the vector field F(x, y) = (sin(x) cos(y), cos(x) sin(y)) conservative? Select the correct answer…

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Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…

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Q: Consider the vector field F = (4x + 5y, 5x + 7y) Is this vector field Conservative? Conservative If…

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Q: . Consider the vector field F(r, y, z) = (8r sin y, 4x² cos y – e"z, –e" – sec² z). 1. Show that F…

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Q: Integrate the vector field h(x,y) = (y^2)i + (2xy-e^(2y))j over the circular arc C parametrized by…

A: Given that h(x,y)=y2i+2xy-e2yj  The parametric equation of the circular arc is  r(t)=cos(t) i+sin(t)…

Q: Consider the vector field F = (x*y, x*y? Is this vector field conservative? Select an answer If so:…

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Q: Consider the vector field F = Evaluate |F · dī along the curve C: F(t) = ti + t°j, 0<t< 2

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Q: Let D be the upper half-plane (y > 0) and consider the vector field F : D+R² given by F(x, y) = (…

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Q: Consider the vector field F and the curve C below. F(x, y) = x2y³i + x³y?j, C: r(t) = (t2 – 2t, t2 +…

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Q: Consider the vector field F = Evaluate F · dī along the curve C: T(t) = t²i + t³ j, 0 <t< 2

A: We have to find line integral.

Q: Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4…

A: we are given the vector field as  F(x,y)=tan-1(2x)4i+(xy-y2+8x2)j to compute…

Q: Let a vector field F(x,y)=sinx i + xy j be given. What is the integral representing the work done by…

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Q: Evaluate F•Tds for the vector field F = x²i- yj along the curve x= y? from (1,1) to (4, – 2).

A: Answer = 19.5

Q: Evaluate the line integral J F. · dr for the vector field F = cos(x)i+ sin(y)j+ x²yk along the curve…

A: Given:  F=cosxi+sinyj+x2yk, rt=t2i+t2j+tk, 1≤t≤3 So, drdt=2ti+2tj+k We know that rt=xti+ytj+ztk So,…

Q: Find the divergence of the vector field V(x, y, z) = -2xi + (y + 5 cos(x))j+ (7z + e8xy) k.

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Q: Consider the following vector field. F(x, y, z) = (2e* sin(y), 7e sin(z), 4e² sin(x) (a) Find the…

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Q: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…

Q: Evaluate F Î ds for the vector field F(x, y) = yì – xj counterclockwise along the circle x² + y² = 1…

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Q: Consider the vector field F and the curve C below. F(x, y) = (4 + 2xy²)i + 2x²yj, C is the arc of…

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