Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2 2 cos 0 3 cos 0 - r 3 cos(03r2) 2 cos 0 r2 r2

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: Find Vf at the given point. f(x, y, z) = 32³ – 2(x² + y²) z + tan '(4xz), (0, 2, 3) Vf\(0,2,3) f(x,…

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Q: Find Wr 0 if W = f(x,y) x=r cos 0 and y = r sin 0, then prove that r Wr 0 =yfx + xfy + xy(fyy-fxx) +…

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Q: By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x…

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Q: Verify the divergence theorem. (a) v = 3r²ê, – rėg + 2êg, V: the cylinder r < 40 < 0 < 2n.0 < z5

A: Given, v=3r2e^r-re^θ+2e^zThe cylinder, r≤4, 0≤θ&lt;2π, 0≤z≤5 According to divergence theorem,…

Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

Q: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

Q: the Following is divergent

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Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

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Q: Prove the Divergence Theorem [3P. + R 2 Pi (0,7) (2,7) (0,0)

A: ANSWER: The given vector is u→=3p1+p2i^+2p1 j^. The region is given by 0≤p1≤2, 0≤p2≤1;

Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = &lt;cos(z), 16y, -xsin(z)&gt; Hence, F1 = cos(z), F2…

Q: tan-i z = ÷In 1-ja sinh-1z = In(z + vz2 + 1) cosh-1 z = In(z + vz² – 1)

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Q: Find the divergence of U = r cos 0 a, – sin 0 a, + 2r² sin 0 ap. r 2 sin 0 3 sin 0 - r2 None of the…

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Q: A) Show that from the lower relations near the point (0,0,0, 0) u can be written as a derivative…

A: Given relations: vcos(y)+xcos(u)=0 ucos(x)+ycos(v)=0 To find the second order Taylor polynomial of u…

Q: . If f = In(x² + y² + y³ ) then find the divergence of falso find its magnitude at 2 3)

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Q: Find the divergence of U=r cos(0)a-sin(0)a+2r²sin (0) a r 2cos (0) 3 cos (0) - r 3 cos (0) - 2cos…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

Q: 10. Show that the function f(x, y, z) = e3z+4y cos 5z satisfies the Laplace equaton. Good Luck.

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Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

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Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: 2 points Divergence of V = e*" î – cos y ĵ + (sin z)² & is ye*y – sin y + 2 sin z cos z O a ye*y +…

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Q: 4. Evaluate the line integral f x siny dx + y dy, where C is the arc of r(t) = ti + t²j from point…

A: Line integral

Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: 3,,5,2, Let F(x, y, z) = (3e*², 4 sin(xy), x³y°z?). (a) Find the divergence of F. div(F) = (b) Find…

A: Given: Fx, y, z=3exz, 4sinxy, x3y5z2 For any given functionfx, y, z=f, g, h divergence∇.F and…

Q: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

A: If fx,y,z =xcos2y-z....icompute dfdx and dfdz

Q: (x) = x and f2 (x) = sin (x) sin Wron

A: f 1 (x) = x and f2 (x) = sin (x) sin Wronskian functions that are linearly independent show using.

Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Prove that v = In [(x-2)^2 + (y - N)^2] is harmonic in every region does not include .the point ( 2,…

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Q: .a. Compute the divergence of the function (V. v) v = (r? cos?0) î + (r² sin²e)ð + (r sin® cosø)

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Q: Using an appropriate linearization, the local linear approximation of f() = T+ cos z at COS I is -…

A: Use linear approximation

Q: Represent f(x, y) (0<x < 4, 0 < y < 4) by a double Fourier series sin (). NTY f(x, y) = EEBmn Sin ()…

A: The given problem is to find the value of Bmn using double Fourier series with given f(x,y) series…

Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

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Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

Q: 1. By using implicit differentiation , find dy/dx for xe^y+ sin xy - ln 2 = -y 2.  find the fourier…

A: Since you have asked for multiple questions, we will solve the first question for you. If you want…

Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: 53. Verify the divergence theorem for A = 2x?y i – y² j + 4xz2 k taken over the region in the first…

A: Given : A=2x2y i- y2j + 4xz2 kbounded by y2+z2=9 and x=2

Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: (z - 1)dt + (1 – t)dz %3D

A: (4) Given differential equation is z−1dt+1−tdz=0......1. We have to determine the whether the…

Q: Defn `x→- `xj diverges to minus infinity" VR>O 3N, such that Vj zN *j<-R 8;<- R Hw7 het x; = - 8j…

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Q: Let f(z) = sin(z'). %3D s'(z) = 3 coslx 3)) 2. 3x cos(X %3D S'(4) = 0

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Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x² -y² .…

A: As per our guideline we can't use any computer algebra. I calculate both line integral and surface…

Q: The Fourier Integral Representation of f(t) is (0, t1 f(t) 1 [sin w + 1 -(cos w wt 1 [sin w + 1…

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Q: 9. Use the divergence theorem to find F.dS where F = ry'i+x sin zj+z°k and S is the surface of the S…

A: use divergence thm and cylindrical coordinate

Q: If D = 10 ρ2 sin2φ aρ + 8 ρ2 cos2φ aφ C/m2 for the region 2 < ρ < 4, 2 rad < φ  < 4 rad, 1 < z  < 2.…

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