b) Use the divergence theorem to compute f. F ·ñ dS, where S is bounded by x + y + 2z = 2 located in the first octant and F = (2x² – y²,4xz – 2y, xy³).

Q: Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

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Q: Consider ∂/∂t f(tx, ty). Prove that if f is homogenous of degree n, then the attatched equation is…

A:

Q: Verify divergence theorem for f=x2i+zi+yzk taken over the cube bounded by x=0,x=1,y=0,y=1,z=0 and…

A: Use the divergence theorem to solve this problem.

Q: R (T) is bounded by its value at the origin i.e., IR, (t)l<Rxx (0) XX XX

A:

Q: 6. Evaluate the line integral F · dr where F = (x³ —y¹, ex²+z², x² – 16y² z²) and C is the curve x²…

A: Thank you,Please rate my response.

Q: 3. Let f (x, y) = 6x³y5 +11x°y* be a given function: a) Find fy and fy, the first partics…

A: the given function is: fx,y=6x3y5+11x6y4 (a) we have to find fx and fy, the first partial…

Q: 2. For F(x, y,z)=[5ysec (xy)+6z°eli+ )- 3 | 5x sec (xy) y 3 k, find the curl and the divergence of…

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Q: conservative.

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Q: z = f(a + y, 2ry) f we take u = x' + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xf.,…

A:

Q: Use the Divergent Theorem to find all values of b> −1 such that ∫∫SFdS = (45b/2) + (51/2), where F…

A:

Q: 5. Let F(x,y,z) = (3xy²)i + (xe²)j+ (z³)k. S is the closed surface bounded by the cylinder y? + z? =…

A: 9π/2

Q: Let D = ((x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 1), C be the boundary of D, and F(x, y) = (2x + y². (x + 1)2 +…

A:

Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

A: The sales of dvds given as the function D = -0.92t + 8.75 and the total sales of streaming videos…

Q: Compute the partial derivative if z = A) - 3ry? B) 1 C) D) Does not exist.

A:

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: 3) Let F = (y+ev=,8x+ cos(y*)) Use a theorem to compute ſ F •dT where c is the boundary of the…

A: Given that  F→=y+ex,8x+cosy3 To compute ∫cF→⋅dr→ where c is the boundary of the planar region…

Q: For the function f(x, y, 2) = 102° y³z+ 7æy®z4 + 19xz2 + 8y%z4 + 5a° + 17y7a11 + 4xyz +23 compute…

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Q: b) Use the divergence theorem to compute ff, F ñ ds, where S is bounded by x+ y + 2z = 2 located in…

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Q: v = 3r?ê, – rėg + 2êz, V: the cylinder r< 40 < 0 < 27.0 < z < 5 V

A: Let, v=3r2e^r-re^θ+2e^z First we identify the components vrr,θ,z, vθr,θ,z and vzr,θ,z of v. since,…

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

A:

Q: Consider the following subset of R^2 De V2/2] V2/2] Let aD be the boundary curve of De. For a = in…

A: Given,            Dc  =x→=xy| x2+y2≥1

Q: Find a norm of the function flt)= t+2t in space C^co13 %3D where normis given by formula ms x…

A:

Q: Find SS, (x2 + y²)dA, where D is bounded by y? = 4x and y = x.

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Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: b) Use the divergence theorem to compute ff, F · i ds, where S is bounded by x +y + 2z = 2 located…

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Q: A2. Use the divergence theorem to evaluate ff, FdS where F = on the surface that consists of three…

A: Given Data: Let us consider the given three surfaces, z=4-3x2-3y2; 1≤z≤4 on the top x2+y2=1, 0≤z≤1…