(§16.4) Compute the work done by the vector field F(x, y) = (sin x + xy², e 9 + 1⁄2x²).. y where Cis the path that goes around with the vertices (0,0), (3,0), (3, 3), and (0, 3) oriented counterclockwise. Answer:

Q: Compute the curl of the following vector field. F= (3x-y,5xy,2) The curl of F is (Di+ (Di+(Ok.

A: F=3x2-y2,5xy,2zCurl F(x,y,z)=∇XF→(x,y,z) where ∇=∂∂xi+∂∂xj+∂∂xkCurl F(x,y,z)=ijk∂∂x∂∂y∂∂zFxFyFz

Q: 2. For the vector field V = (7x³ + 2y2²)i + (4x²z - 7y²+3)j + (4y³ +2² -32²) k find the divergence…

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Q: 1. For each curve, construct dr. • Let C1 be r? + y? = 16 • Let C2 be y = 5 – 2x • Let C3 be r = 2 –…

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Q: 1) Find the length of the function r = (1+ 2t, 3 – 2t, v2t²) on 0 <t < 1. %3D

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Q: 41.) Use given grid to sketch the vector field F = (y, -x). Include vectors at all integers points…

A: Given vector field is F=12y,-x

Q: Represent the following equations in R? by a vector-valued functions. Imet gaoglecomis shwing your n…

A: Given

Q: Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂ be the parabola…

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Q: Graph

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Q: Find the domain of the vector functions, r(t), listed below. You may use "-INF" for -∞ and use "INF"…

A: We have to find the domain of vector function.

Q: E and F are vector fields given by E = 2xa¸ + a, + yza. and F = xya, − y²a,+ xyza. Determine: (a)…

A: Given: Two vector fields: E : 2xax+ay+yzaz F : xyax-y2ay+xyzaz To find: a) E at 1,2,3. b) Component…

Q: y = C1 cos 3x + c2 sin 3x => y" + 9y = 9

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Q: Match the graph with the vector field: F₁ = , F₂ = , F3= , F4 = 0 (A) 2 2 0 2

A: We are given vector functions F1=2, xF2=2x+2, yF3=y, cosxF4=x+y, x-y

Q: Which vector field would generate this graph? 0( - y, – a) O (y, z) O (x, – y) 0( - 1, y)

A: We check the given vector field one by one. First one is fx,y=-y,-x Now, for point 1,1 we see that…

Q: Sketch the vector field. 8 2 0 -2 0 y 0 2 0 -2 F(x, y) = (2, 2) = 2'

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Q: Match each vector field with its graph. ? 1. F(x, y) = x² + yj ? ? 2. H(x, y) = x² - yj 3. G(x, y) =…

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Q: Consider the functions below. F(x, y, z) = xizj+yk r(t) = 4ti + 6t j - t² k (a) Evaluate the line…

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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: Consider the square C oriented counter clockwise, with vertices (0, 0), (2, 0), (0, 2), (2, 2) and 7…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: 3.For the vector field F = 2(x + y) - 9 2x² + 2xy, › evaluate fF.ds where S is the upper hemisphere…

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Q: V(E × F) = F(V × E) – E(V × F). %3D

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Q: 6. A mountaineer is She begins her jo (a) Calculate th

A: Directional derivative at point is obtained by derivation of the function at x and y variables or…

Q: Let a vector field F(x,y)=sinx 1 + xy j be given. What is the integral representing the work done by…

A: Acoording to expert guidelines, I am allowed to answer first question only. Kindly repost the rest…

Q: Sketch the given vector fields by drawing some representative vectors. (a) F(x, y) = (x − y) î+xî…

A: Given:  a F→x, y=x-yi^ +xj^b F→x, y=y, -xx2+y2c F→x, y=2yj To sketch the given vector field.

Q: (20) Given the vector field i = (a² – y² + 2xz)î+ (xz – ry + yz)ĵ+(2² + x²)k. Find v x ở and show…

A: Given v→=x2-y2+2xzi^+xz-xy+yzj^+z2+x2k^

Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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