If divF (x, y, z) = 0 for all (x, y, z), then curlF (x, y, z) = (0,0,0) for all (x, y, z).

Q: biven that y=sin(3lncx)) is a solulion of x y" + xy' +9y=0, solue x y"+ xy' +qy=0 ; y()= 2 =y'().

A: Solve Cauchy Euler differential equation

Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: exist. :) Compute the linearization of f(x, y) at the point (x, y) = (1,1). %3D

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Q: Use the chain rule to find where g(u,v) = f (x(u,v),y(u,v)), f(x,y)=xy³ -4x² , ög ди x(и, у) -и*…

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Q: Find div F and curl F if F(x,y, z) = x°i – 11j + yzk. - div F= curl F=

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Q: Usando la fómula de reducción de orden, determine una segunda solución en: x'y "-5xy' + 9y = 0 ; y,=…

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Q: Iculate O F- dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

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Q: of of Find and for the furction f(xy,z) = x y+ y + xỉ ôx 'ay

A: For the function f( x, y, z ) = x2y + y2 + xz2 . We need to find some partial derivatives.

Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: [Find div(F x G) and Curl (F x G) where F(x, y, z) = x²yi + y³z²j – 2z²k | and G(x, y, z) = 3xyi –…

A: Given Fx,y,z=x2yi+y3z2j-2z2kGx,y,z=3xyi-5yzj+4z2k

Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

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Q: Bounded by the planes z= x, y =x, x+y=2 and z= 0

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Q: Find div F and curl F if F(x, y, z) = 10y³zºi – 8x³z¹ºj – 5xy³k. div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = x²i – 7j + yzk. div F= curl F=

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Q: De'Morgan Theorem to prove that: (x.y'+x'.y)' = x.y+x’.y' %3D wwww

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Q: Find div F and curl F if F(r,y, z) = 1°i – 7j + yzk. div F= curl F=

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Q: If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y,…

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Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)-1 a(x,y)'a(u,v)

A: Given: x=u1-v,  y=uv To verify ∂u,v∂x,y×∂x,y∂u,v=1

Q: Find div F and curl F if F(x, y, z) = 17y*z4i – 3x°z®j – 3xy°k. - div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = 9y¹zºi – 14x³z7j — 5xy³k. div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = xz¹i+ 4ya²j+6z²yk. div F= curl F=

A: Vector

Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 5y*x²j +4z²yk. div F= curl F=

A: To find curl F and div F.

Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

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Q: Let F = (2yz – 3x) i + (3xz + 3y) j – (2xy+ ∞z) k. Find div F and curl F.. |

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Q: Find div F and curl F if F(x, y, z) = 17y*z*i – 3x'2ºj – 3ry®k. div F= curl F=

A: Let's find.

Q: Write the chain rule for- at aw given that w = f(x,y,z); x = g(t), y = h(r,t), z = k(s,t)

A: We are given that w = f(x, y, z), x = g(t), y = h(r, t), and z = k(s, t). We need to write the chain…

Q: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

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Q: Calculate div(F) and curl(F).  F =〈x^2, y^2, z^2〉

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Q: let f (x, y) = x² + xy + y². Using the chain rule, calculate %3D af -(u(x, y), v(x, y)) being u = v…

A: Given that                                   f(x, y)=x2+xy+y2 And also we have…

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – z, z – x, x – y), then div(curlG (x, y,…

A: given statement if false.

Q: linean trensformabe which af the Pollowing ý a Pixiyiz) =(xyt, x+y, x+2, YtZ) PXIYA) =(2x,2y 12Z,…

A: Note:- 1) Due to our guidelines we can solve only 1 question. 2) In question 1) there is a…

Q: u:(x, t) = и (т, Urz(T, t) u,(0, t) = uz(1, t) = 0 u(x,0) = f(x)

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Q: Find curl curl (5z i + 6x j + 8y k) i 5 i i 6 (5z i + 6x j + 8y k). 8 = ( )i + ( )j + ( )k

A: Given that a vector 5z i^ + 6x j^ +8y k^ We have to find a curl of this given vector. Curl of a…

Q: g) div(7) for 7(x, y,z) = xyi + yz²j +x²yzk h) curl(ï) for ū(x, y, z) = xzi + xy²j+y²zk

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = x*i – 11j + yzk. div F= curl F=

A: Vector

Q: Find div F and curl F if F(x, y, z) = x°i – 10j + yzk. div F= curl F=

A: To find the divergence and curl of the following vectorF→=x9i-10j+yzk

Q: Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

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Q: Theorem:For all Xiyiz,w EN i) X<y ^ z sw =)x+Z <ytw ii) xsy ^ zw =) x+Z< y tw )x<う tsw 1 Esw うメ+ と x…

A: Solution: We know that for x,y∈ℕ If x&lt;y then ∃k∈ℤ+,k&gt;0 such that x+k=y If x≤y then ∃k∈ℤ+,…

Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

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Q: Find div F and curl F if F(x, y, z) = xºi-7j+yzk. div F= curl F=

A: Given that F(x,y,z)=x6i-7j+yzk. The objective is to find divF and curlF.

Q: Find div F and curl F if F(x, y, z) = xªi – 2j + yzk. div F= curl F=

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