Find the absolute maximum and absolute minimum of f(x, y) = yx² – y² +4 on the unit disk {(x, y) : x² + y² <1} |

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Q: find the absolute minimum and maximum of f(x,y)=2x^3+y^4  over the disk x2+y2 ≤ 1

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Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Integrate F = 3x2yi + (x3 + 1)j + 9z2k around the circle cut from the sphere x2 + y2 + z2 = 9 by the…

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Q: A solid lies above the cone z = V x² + y2 and below the sphere x2 + y2 + z2 = z. Write a description…

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Q: Find the absolute maximum and absolute minimum of f(x, y) = yx^2−y^2+4 on the unit disk  (x, y) :…

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Q: (a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-disk x² + y? <…

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Q: At what points (x, y, z) in space are the functions continuous?  a. ƒ(x, y, z) = x2 + y2 - 2z2 b.…

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Q: (a) Between 1 and the disk x²+ (1+x² +y*) (b) Between % = 1 and the entire xy-plane. (1+x* + y?)*

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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Q: ind the maximum value of the function f(x,y,z) = x² + y² + z² on the plane x+y+z = 1.

A: The given function is; f(x,y,z) = x2+y2+z2

Q: Calculate F- dS where F = (e" sin y, e* cos y, yz²) S is the surface of the box bounded by the…

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Q: Use a parameterization to find the flux do of F = z²i+ xj – 4zk in the outward direction (normal…

A: Apply Divergence theorem to the given surface integral, ∬F.ndσ=∫∫∫DivFdV

Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

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Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Determine the absolute maximum of f(x, y) = x² + y² – x – y + 2 - on the unit disk D = {(x, y) : x²…

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A: Given  F(x,y) = 2xyx2+y22i+y2-x2x2+y22j To Evaluate  ∫CF(x,y)dr

Q: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

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Q: (7) , Find the absolute maximum and absolute minimum of f(r, y) = ya? - y? +4 on the unit disk {(*,…

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Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: Let f(x, y) = x² + y² – 2a°y- if (x, y) # (0,0), - (14 + y²)² ' and f(0, 0) = 0. Show that f is…

A: Given: fx,y=x2+y2-2x2y-4x6y2x4+y22 if x,y≠0,0 and f0,0=0.   To show: (a.) f is continuous at the…

Q: 5. Find the flux of F (x,y,z) = y cos(z)i-yx sin(x) j+ xy³k through the outward oriented cube of…

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Q: find the absolute maximum and minimum of the function f(x,y,z)=x+2y on the intersection curve…

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Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: (x,y,z)D X22+zy 13D use Dvergence Theovem to find tward Sof the Solid G bounded x-1 %3D xy-Plane

A: we have to find the flux for the vector field  F(x,y,z)=xzi+zyj+2z2k across the surface bounded by…

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Q: Integrate the function f(x, y, z) = (x2 + y2 + z2)4 over the part of the solid cone y2 + z2 ≤ x2…

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Q: find the flux of f=zk across the portion of the sphere x2+y2+z2=a2 in the first octant in the…

A: Given the field, F=zk The surface S is the portion of the sphere x2+y2+z2=a2 in the first octant in…

Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

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Q: Find the maximum value of f(x,y,z)=24x+18y+21z on the sphere x²+y²+z²=49 I

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Q: Find the flux of F(x,y,z) = (-x,-y, z³) , across S. Where S is the part of the cone z = /x² + y²…

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Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Find the flux of F = (x - y)i + xj across the circle x2 + y2 = 1 in the xy-plane.

A: Given F = (x - y)i + xj  across circle x2+y2=1

Q: 2. Use the Divergence Theorem to calculate the flux of F(x, y, z) = (x³ + y) i+(y³ + 2³) j+(z³ + x²)…

A: The given vector field is  F(x, y, z) = (x³ + y) i+ (y³ + z³) j+(x³ + x²) k across the surface of…

Q: Find the maximum value of P.F•dr, where F = 6xy?i + (3z - 10xy²)j+ (4y – 2x²y) k and C is a simple…

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