F(x, y, z) = ryzi + yj + zk %3D

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Find div F and curl F if F(x, y, z) = 14y°z4i – 3x°z+j – 3xy'k. %3D div F= curl F=

A: Given that,Fx,y,z=14y6z4i-3x3z4j-3xy3k

Q: A F²(xy, 2) = x₂ ₁ + x² ² + x ₂7² [ z) xy Find div F and curl I at (1,1,0) 0

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Q: Find div F and curl F if F(x, y, z) = 11y°z'i – 14.x°z°j – 7xy*k. | div F= curl F=

A: Given problem:- Find div F and curl F if F(x, y, z) = 11y5 z7 i - 14x6 z8 j – 7xy4 k.

Q: Find div F and curl F if F(x, y, z) = 6e#Y i – 7 cos yj+ 9 sin² z k. 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: Liv F and curl F if F(x, y, z) = xºi - 2j+yzk. F= F=

A: Topic:- application of derivatives

Q: Find div F and curl F if F(c, y, z) = 10e*Y i – 9 cos yj+ 4sin? z k. div F= curl F=

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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: Find div F and curl F if F(r, y, z) = 8y'2°i – 17x*2°j – 4xy k. div F= curl F=

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Q: Determine the y-coordinate of the centroid of the shaded area. b 1 x=y²/b 0.63b

A: Consider the following figure. Equation of straight line is y=1−0.63x=0.37x. For a thin strip…

Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

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Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: Find the curl and divergence of F(r, y, z) = (e**, -2e"², 3.xe"). Please show steps/explain

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+ 5z'yk. ,62 div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x*j+22²yk. div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = 10e*Y i – 6 cos yj+ 2 sin? z z k. div F= curl F=

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Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i +5xj + 3yk G(x, y, z) = xi - yj + zk

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Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

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Q: Find div F and curl F if F(x, y, z) = 4y°z°i – 8a*zl°j – 7xy°k. div F= curl F

A: we have to find curl and divergence of F.

Q: Find div F and curl F if F(x, y, z) = 17y®z*i – 8x'z®j – 4cy°k. %3D - div F= curl F=

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Q: Find div F and curl F if F(r, y, z) = xz'i+ 4y*x*j+ 62²yk. div F= curl F=

A: F(x,y,z)=xz3i+4y3x2 j +6z2 yk The aim is to find div F and curl F.

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x²j+ 22²yk. %3D div F=|2 + 12 y² x² + 4 z y curl F=|2…

A: Find div F and curl F

Q: Find the curl of F. F(x, y, z) = (x cos(y))i + xy²j

A: For curl of vector, we do cross product.

Q: Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=

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Q: z+y? for F (x, y, 2) = ( ?y° z, Va + y+ z, at the point (1, 1, 1) find the exact answer (on the…

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Q: Find div F and curl F if F(x, y, z) = 15y^z*i – 11a°2°j – 5xy°k. - div F= curl F=

A: Here the given function is F(x, y, z)=15y4z4i^-11x6z6j^-5xy3k^ We have to find div F and curl F.

Q: Use cylindrical coordinates. Evaluate V x2 + y2 dV, where E is the region that lies inside the…

A: ∫∫∫E x2+y2 dv= ∫∫∫ x2+y2 dx dy dzPut                   | Thenx = r cos θ     | dx dy = r dr dθy = r…

Q: Find div F and curl F if F(x,y, z) = 9e*Y i – 8 cos yj+ 4 sin? z k. %3D div F= curl F=

A: F(x,y,z)=9e^(xy)i-8cosyj+4sin^2zk ∇F=∂F(x,y,z)∂xi+∂F(x,y,z)∂yj+∂F(x,y,z)∂zk…

Q: Find div F and curl F if F(x, Y, z) = 11y°z°i – 3x*z°j – 6xy°k. - div F= curl F=

A: The given vector function is: F(x,y,z)=11y6z5i-3x4z6j-6xy3k Let, F(x,y,z)=F1i+F2j+F3k then…

Q: ppose z = f (x, y), where x = rs and y =r+s. Find zZrs in terms of fæ, fæx, fæy, and fyy.

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

A: Divergence of F: ∇·F=i→∂∂x+j→∂∂y+k→∂∂z.i→17y4z4-j→3x3z6-k→3xy6 ∇·F=∂∂x17y4z4+∂∂y-3x3z6+∂∂z-3xy6…

Q: Find div F and curl F if F(x, y, z) = 5y*z*i – 17x°z*j – 4cy°k. %3D -

A: Given F(x,y,z)=5y4z4i-17x6z4j-4xy7k We need to find div F and curl F

Q: Q4/ Find the centroid of the shaded .area shown in figure below y =4² b.

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Q: Qs/ Locate the centroid xc and ye of the shaded area. y2 = 4x %3D 2 m y = 2x

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Q: F(x, y, z) = 4e"z+z7+2z cos x3 – sin zk 7 is the paraboid x = 4 – y? – z?, x < 0, oriented with a…

A: Stokes theorem to evaluate the surface integral as line integral.

Q: Find div F and curl F if F(c, y, z) = 5y°z'i – 14x°z°j – 5xy°k. div F= curl F=

A: F(x,y,z)=5y6z7 i -14x3z5 j -5xy3 k The aim is to find div F and curl F.

Q: Find div F and curl F if F(x, y, z) = 10y°2³i – 11x°z!°j – 3xy°k. „10: div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = 12y"2³i – 3x"z+j – 4xy°k. div F= curl F=

A: A detailed solution is given below

Q: Find div F and curl F if F(x, y, z) = 17y°z*i – 8x°z°j – 3xy°k. „6: div F= curl F=

A: Given that: F(x,y,z) = 17y3z4 i  - 8x6z6 j - 3xy3 k To find: Divergence (div) of F Curl of F

Q: Find div F and curl F if F(x, y, z) = 13y°z³i – 9x*z³j – 4ry°k. div F= curl F=

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Q: FIND V= (eX*z) čx + 2xy Èy+(xyi z³) &z THE CURL OF

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Q: Find div F and curl F if F(x, y, z) = 13y z'i – 13x°2°j - 4xy°k. div F= %3D curl F-

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Q: Find curl(curl F) = x (V x F). F(x, y, z) = 4x³yzi + yj + 4zk

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Q: Find div F and curl F if F(x, y, z) = x¹i − 6j + yzk. - div F= 7x + y curl F zi X

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Q: Use a parameterization to find the flux F•n do of F = 6xy i – 5z k outward (normal away from the…

A: We have,

Q: F = xzi + xyzj - y?k, find i. V•F ii. V x F i. div(curl F)

A: Given F=xzi +xyz j-y2k        ∇=i ∂∂x+j∂∂y+k∂∂zi ∇.F=i ∂∂x+j∂∂y+k∂∂z.xzi+xyz+jy2k…

Q: Find div F and curl F of F(x, y,z) = (x z³) i + (3x²y1² )j + (3z?y) k

A:

Q: Find curl(F x G) = V x (F x G). F(x, y, z)= i + 7xj + 6yk G(x, y, z) = xi - yj + zk

A: