T0.Tind the nux of the vector field k- across the sphere of radius R centered at origin, where F=(x,y,z) is the position vector ( Ans: 47TR*k) 17. Verify the Gauss Divergence theorem for the vector field F = k-, over the surface of the sphere x +y² +z² = R² where F = (x, y, z) is the position vector. (Ans: 4tR*k) %3D 18. Find the flux of the water through the parabolic cylinder y =x, between the planes x=0,z=D0,x%=3,z=2, if the velocity vector is F = yî+2j+ xzk m/ sec. (Ans: 69 m / sec %3D ) 19. If F =(2x-y+2z)î+(x+y-z)ĵ+(3x-2y-5z)k , calculate the circulation of F along the circle in the xy-plane of radius 2 and centre at origin. ( Ans: 87) 20. Using Green's theorem find the area of the region bounded by y=x and y =x+2.( Ans: 9/2) Scanned by CamScanner

Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If…

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Q: Find the divergence of the vector field F(x,y,z) = (ye*,2x + 3y, ycosx).

A: Consider a vector field is defined as, Fx,y,z=f,g,h The divergence of the vector field is defined…

Q: Find (a) the divergence of the vector field and (b) the curl of the vector field.

A: Given :   To find : a) The divergence of the vector field. b) The curl of the vector field.

Q: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

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Q: For the vector field F(x,y,z)=ya'1+x1+2xyz k a) show that F is conservative vector field; b) find a…

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Q: Find the divergence of the vector field F. F(x, y) = 3x2i + 5y?j %3D

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary…

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Q: (a)the curl and (b)the divergence of the vector field. F(x,y,z)= ln(2y+3z)i+ln(x+3z)j+ln(x+2y)k

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Q: Use the divergence of the vector field to compute F(x, y) = (tan-¹ (2x) fo tan¯¹ (2x) 4 where is the…

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Q: Find the divergence of the vector field F = < ya®, æ2®, zy* div F = Preview

A: Divergence of F→=yx3, xz6, zy4

Q: (a) Is the vector field F(x, y) = (xe³, ye²) conservative? Justify your answer. If it is…

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Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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Q: Find the divergence of the vector field F→(x,y,z)=7sinxi→−cos(3y)j→+z^9k→.   Enter the exact…

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Q: 4 Consider the force field Ġ(x, y, z) = (- ze² -*, 2ze²y-x, e²y-x z²+2z+2 a. Determine whether the…

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Q: Consider the vector field F(x, y, z) = (ycosh x + ze*, sinh x – 3z³, e* – 9yz²) a. Find the…

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Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: For vector field F(x, y, z)=(1+ 9xry, 3x +e, ye' +2= (a) Carefully calculate curl F. (b) Find the…

A: We have to calculate curlF  and total work

Q: Consider the vector field F (x, y, z) = (ycosh x + ze*, sinh x – 3z3, e* – 9yz²) %3D a. Find the…

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Q: Verify Stoke's Theorem for the vector field F = (2y + 2) i + (x –2)ĵ+(y – x) . over the portion of…

A: The formula for stokes theorem is, ∫Pdx+Qdy+Rdz=∬∇×F.ndS Given that, F=(2y+z)i+(x-z)j+(y-x)k Then,…

Q: Consider the vector field F = (r'y*, z*y") Is this vector field Conservative? Select an answer v If…

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Q: Consider the vector field F = 2xy i + (x2 + 2y) j. Verify the Green's Theorem in the closed region…

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Q: Evaluate the line integral F dr where the vector field and the curve are defined as follows: F(x, y,…

A: Given problem:-

Q: Ex: Find the work done by the vector field F = (y-x²)i + (z - y²)j + (x-z²2)k Over the curve r(t) =…

A: Given: F=y-x2i+z-y2j+x-z2krt=ti+t2j+t3k

Q: Q3 Vegify Stokes theorem for the vector field x* +y'+z Vesty.2tokes theorem for the vector field F=…

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Q: Q5. Consider the vector field F(x, y, z)=xi + 2yj + (x² + 4y²) k and the closed surface S made up of…

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Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: Consider the vector field F (xr, y) = (2y - 12r*y", 4ry – 9r*y?) is conservative. (a) Show that F…

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Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…

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Q: Find (a) the divergence and (b) the curl of the vector field F(x, y, z) = cos(z)i + 5ysin(5z)j+…

A: Given vector field is  F(x,y,z)=(cosz)i+5ysin(5z)j+2x2zk

Q: - L ---- Let F be the vector field (r², 2r, z²). Let C be the boundary of the surface S given by 4x²…

A: Given- Let F→ be the vector field x2, 2x, z2. Let C be the boundary of the surface S given by 4x2 +…

Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

Q: Consider a force field F = yi+zj+k that acts along a path from foothill A to the top B as in the…

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Q: Consider the given vector field. F(x, y, z) = (In(x), In(xy), In(xyz)) (a) Find the curl of the…

A: Given vector field: F(x,y,z)=ln(x),ln(xy),ln(xyz)

Q: Find the divergence at (15, 0, 0) for the vector field F(x, y, z)= e*sinyi-e cosyj+z²k O 16 O 451 30…

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Q: Consider the vector field F = (x*y, x*y? Is this vector field conservative? Select an answer If so:…

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Q: 3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo…

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Q: 4 Consider the force field Ğ(x, y, z) = = = -ze²y-x, 2ze²y-x, e²y-x 2² + 2x + 2 a. Determine whether…

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Q: 21. Compute the flow of the vector field F = r through the surface of the ellipsoid y² + 2 = 1 in…

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Q: Consider the following vector field. F(x, y, z) = xy2z2i + x?yz?j + x?y?zk (a) Find the curl of the…

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Q: Find the divergence of the vector field V(x, y, z) = -2e*'i – e³xyj+ 7e%yzk.

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Q: 4- Evaluate the surface integral of the vector field F = [ax, by, cz] over the sphere r² + y² + 2² =…

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Q: Consider a force field F = yi+zj+k that acts along a path from foothill A to the top B as in the…

A: Given - F=yi+xj+k  Surface of mountain is the graph of the function- z=1-x2-y2 To find - Work done…

Q: Given the following curve: 7: [0, 1] → R? kt² tHy(t) = 3t2 +2 and the following vector field: R? →…

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Q: 3. What is true about the value of F.dS for the vector field F (r'y,-ry,-I*yz) where S is the…

A: Solution 3: Given  F=x3y,-x2y2,-x2yz We have to calculate ∬SF.dS, where S is the surface of…

Q: Q5: Find the divergence of the vector field y F(x, y, z) = x² √yi + =j+zk At the point (2,4,1).

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Q: Find the divergence of the vector field V(x, y, z) = -2xi + (y + 5 cos(x))j+ (7z + e8xy) k.

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Q: Consider the following vector field. F(x, y, z) = (2e* sin(y), 7e sin(z), 4e² sin(x) (a) Find the…

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Q: Consider the vector field F (5x+6y, 4z +5y) Is this vector field Conservative? Select an answer v If…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.