Consider the vector field F(x, y, z) = (3z + 4y)i + (3z + 4x)j + (3y + 3x)k a) Find a function f such that F = Vf and ƒ(0, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0, 0) to (1, 1, 1). Use part a) to compute the line integral SF · dr.

Q: 4. Solve the following equation by transforming the Method Laplace (Transform) transform. u(x)= x -…

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Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: Find the directional derative of f at the point P0(1,1) in the direction of the vector A = 3i - 2j…

A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: Find the domain of r(t) and the interval(s) on which the vector- valued function is continuous. r…

A: We need to find the domain and the interval on which the vector-valued function is continuous.

Q: For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in…

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Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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Q: The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end…

A: Given, vector field F→x,y=2xy,x2 and three curves that start at 1,2 and end at 3,2.

Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

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Q: Let f(x, y, z) = x²y - xy² + z³, P(1,1,2), u is the vector from P to Q(1, -2,-2). Determine the…

A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: 2. For the vector field F(x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div…

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Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: For the vector-valued function r(t) = t³i + (2t² + 1)j + (3t − 6)k find the following and express…

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

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Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: Prove that (Y - Y1)'(Y - Y1)= (-Y1)'(- Y1) + (Y-P)'(Y-P) where Y = n 1 Y and 1 is an n-dimensional…

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Q: Sketch the vector field: F(x, y) = (1, 2y) Carefully draw at least four vectors in each of the four…

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Q: The position of a particle is determined by the vector-valued function r(t) = (1 - 12,3t, 1³). Find…

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Q: F(x,y) = (4xy. – 3y²) (A Vxi = -4x B) V XF - - 2y C vxF V xF - - 2y + 8x D VxF - 4x - 6y

A: solution

Q: Find the curl of the vector field F =< yx5, xz², zyб curl F = i + 1:0 12

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Q: Suppose f(x, y) = √tan(x) + y and u is the unit vector in the direction of (1, 1). Then, (a) ▼ ƒ (x,…

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