. Consider the vector field F(r, y, 2) = (8r sin y, 4x² cos y – e"z, -e" – sec² z). %3D | F. dR where C is any smooth path from (1, 5,0) to (2, 0, 7). Evaluate

Q: (x, y) (1.0) (2, 2) (3,0) (0, 1) (-2,2) (0, 3) F(x, y) (0, 1) (-2,2) (0.3) (-1,0) (-2,-2) (-3,0)…

A: This is a question of vector calculus.

Q: 5. Consider the vector field F(x,y,z) = yzi + xzj+(xy+2z) k and the curve C given by r(t) = (t+ sin…

A: Given vector field: Fx,y,z=yzi+xzj+xy+2zk Curve C is given by: rt=t+sin12πt,t+cos12πt,2t,   0≤t≤1…

Q: ey+y°.

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Q: Calculate the divergence of the vector field F (x, y, z) = − 10 sin(2xy)i — cos(x³y)j. (Give an…

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Q: How much work is required to move an object in the vector field F= 5 y2i + 2xy J  Along the curve ,…

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Q: Let F be the vector field (ze"+yz², xz², xe"²+2xyz) Let C be the path r(t) = (sin(t), teʻ, cos(t)),…

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Q: 1. Find the line integral in a vector field a curve consisting of 2 parts. First, the straight line…

A: Given F→=y,x+2y We have to find the ∫CF→⋅dr along the given path.

Q: y² cos(xy?) – ay sin(æ²y) Let it be 7 : R² → R², (2ary cos (ay?) – ža² sin(a²y)/ a vector field.…

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Q: 7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where F2…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Let C be the curve with parametrization r(t) : ,0 . Find the value of F · dr.

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Q: The gradient of f (x, y) = x sin (y²) is the vector field F(x, y) = at (2,√7/6) and ending at…

A: The given scalar function is, f(x,y)=xsiny2. Gradient of this function is F=siny22xycosy2. The…

Q: 1. Consider the vector field F(r, y, 2) = (* - ", e – a*, z – sin(ay2). (a) Sketch the vector field…

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Q: Sketch the slope field for the points (ti, y;) where at and dy dt y-2 Z₁ = -1 + 0.25(1-1) = for…

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Q: For vector field F = (-2y, y), y > 0. Find all points P such that the amount of fluid flowing into P…

A: The vector field given is as follows: Fx, y=-2y, y We are asked to find points P=x, y such that the…

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: 2. Let F(x, y) -yi-zj + zk be a vector field. Compute F FdS, where S is the hemisphere a² + y² +₂²…

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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: (a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) (1,2,3). Using the G from part…

A: We are given the vector field  G=xyz,yz,xzwe have to find the divG , line integral ∫cG.dr for line…

Q: Consider the function f(x, y) = exy. (a) (b) (c) Determine the vector field F = Vf. Evaluate F. dr…

A: (a) ∇f=fxi+fyj (b) A gradient field is always irrotational so its integral will be path independent.…

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

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Q: Let be a potential for the vector field F = (-24 x³z + 6 xyz², 3 x² z² + 15y¹, −6 x¹ + 6 x²yz - 10…

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Q: Determine the vector field of F. F(x, y) = yl – x) 1.

A: Vector field