(х, у) F = x² + y²" for x > 0, y > 0

Q: 4. Consider the vector field given in Cartesian coordinates by A(r) = (x² + y³, 3xy², z²). (a)…

A: Given : Ar=x2+y2,3xy2,z2

Q: a² dq er f(q)

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: three decimal pI 1.1 ,Yi = i 2.51 X2 = i 1.2 ,Y2 = i 3.273 X3 = i 1.3 Y3 = 4.50283 X4 = i 1.4 Y4 =…

A: Consider the equation

Q: Stoke's theorem

A: We have to verify the Stoke's theorem for the given vector field. It is given that

Q: 3. а. Given a potential function/- Ax'y*z' - Bx"y'z -Cx'y'z, where the coefficients 4.B.c, are the…

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Q: (b) The square with vertices (0,0), (1, 0), (1, 1) and (0, 1), and the vector field F = 3x²yi + x³j.

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Q: (e) Verify Green's theorem for a vector field F(x, y) = y²i + x²j and a triangle bounded by the…

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Q: d) Use the curl test to determine if the following vector fields are conservative on R². If the test…

A: As per our guideline we can solve only first three subparts question. Let a vector field    F=…

Q: 3. a. Given a potential function f = Ax°y*z³ - Bx°y°z² -Cy°z, where the coefficients 4,B.C, are the…

A: For any conservative vector field there is a scalar potential function.

Q: A two-dimensional vector field describes ideal flow if it has both zero curl and zero divergence on…

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Q: Calculate the curl and divergence of each of the following vector fields: 3.1. F= (2.xy + z³)…

A: You asked multiple questions, and not mentioned which question you need answere. So according to…

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: Determine if the vector fields below are conservative. Find potential functions where possible. (a.)…

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Q: (xy³ +3x²y, 3xy² + x²) 2+x ху у,

A: According to question given that Vector Field F⟨xy3+3x2y, 3xy2+x2⟩

Q: Verify that the following vector field is conservative and then find the corresponding potential. F…

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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: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: x-z+4 8x-y+3z² 3. Given vectors field G = 3* 4+z2 :ax + y3+z - ay and a position vector, r, = 2ax –…

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Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: Identify whether the given vector field has positive, zero or negative divergence. Zero Postive…

A: We need to determine if the divergence of the given vector field is positive, zero or negative. The…

Q: 2. A vector field is specified as G = 24xy ā, + 12(x² + 2)ā, + 18z²ā,. Given two points, P(1, 2, -1)…

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Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):