O Verify the divergence theorem of cadius 2. out ward normal vedar, and vecfor field for a Sphrere Ê =(y +ak).

Q: x' = -x 22. Find homeomorphism H for {y = y +x³ near origin.

A: Given that  x'=-xy'=y+x3 The solution for x'=-x is x=Ae-t The solution for y'=y+e-3t is,…

Q: If f(x, y) = x²y+ y² and F(r, y) = Vf(x, y), find Fo F(1, -2). %3D Select one: a. (-12, 0) b. (16,…

A: We have given multiple choice question each having one option correct based on the function gradient…

Q: Draw the slope field (direction field) for the following DE: y'=y-t

A: Given DE is Make table as follows:…

Q: 4. Find the divergence and curl of the following vector function: F(x,y, z) = ( arctan(ry),…

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Q: Find the wark done by the Foree Field FoK x>ye^> along the parabola X=y+1 from (bo) to (2,1).

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Q: Suppose the slope field given below is for the equation u' = f(t, u). Draw a possible solution for…

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Q: dy Sketch a slope field for = X dx isoclines. 3y showing a table of dy/dx and 5

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Q: Is the vector field F(x, y) = (In y + sin(e²“), #

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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: Suppose f(x, y) = x² + 2æy+ y². Which field plot is Vf? Justify your answer. 鹿

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Q: That is not what I needed. I needed a FIGURE, a SLOPE FIELD given the initial conditions. Possibly…

A: As per the question we are given a nonlinear dynamic system depicting a predictor-prey model as :…

Q: Give conditions on a, b and c so that the line integral of the vector field F = ai + bj + k on the…

A: According to question given thatF→=ai→+bj→+k→C is the segment from (1,4,1) to (1,4,c)

Q: For Vector fields with va (X.X)= x VY (X. y) = y X U* (x.y) =~Y U (x.x) = x Compute the Lie…

A: Given: Vector Feilds with Vxx.y=x   Vyx.y=yUxx.y=-y  Uyx.y=x We need to compute the Line derivative…

Q: Find the divergence of the vector field F = div F = %3D

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Q: Determine the signs of the line integrals for the pictured vector fields and curves. C₂ (a) (b) C₁…

A: The sign of line integral decided with the help of angle formed by curved and vector filed. Since…

Q: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

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Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

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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: consider che funceion h= w²-8.Tawei Determine dh/dt and w= St"-26

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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: 6. Show that a constant force field does zero work on a particle that moves once uniformly around…

A: We have to prove that constant force field does zero work on on a particle that moves once uniformly…

Q: CLO 5 For the conservative field A=1x a, 8y a. The line integral f. A.dl where c is the line segment…

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Q: Find the divergence of the vector field F = . div F=

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Q: z = 0 and z= 2. Compute JJ FdS, where S is the surface of the cube bounded by the planes x = ±1, y =…

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Q: C

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Q: 1. Let f(z,y) = cos(z - y) and C be the line segment from (-1,1) to (3,-2). Set up but do NOT…

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Q: ff curl(x²yi - rzk). n do over the closed surface of the ellipsoid 4 16 Warning: Stokes' theorem…

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Q: 1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line…

A: Consider the provided question,

Q: Q. 10: If o = 4x'y3 z5 then Find divergence of gradient of p. %3D

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Q: What does the slope field for dy eay look like? dr where a < 0 (that is: it's negative).

A: Given that:dydx=eay