Use Stoke's theorem to evaluate F dr where F(x,y, z)=e-7i+ +e"k and C is the boundary of the part of the plane 8x +y +8z =8 in the first octant. O 23 O 49 O 69 O 16

Q: Find the surface area for the portion of the surface f(x,y)=1-x² + y that lies above the triangular…

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Q: b) Use Gauss' theorem to evaluate ff F - ndS where F = (r - y)i + y²j+ (ry-y)k and o is the closed…

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Q: Stokes' Theorem to evaluate F dr where C is oriented counterclockwise as viewed from Jc F(x, y, z) =…

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Q: Let F(r, y, 2) = (r² – z², y, 2rz), and C be the boundary of the piece of the plane r+y+z= 4 in the…

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Q: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

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Q: (c) Use Green's Theorem to evaluate (3xydx+ 2xy dy, where C is a counterclockwise oriented…

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Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

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Q: Evaluate the surface integral xyzdS where S is the part of the plane z = 1 + 2x + 3y that lies above…

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Q: Let G be the solid enclosed by the plane z= y, the xy-plane, and the parabolic cylinder y = 1-x². If…

A: Consider the given information,

Q: Identify the theorem: If S is the boundary surface of a solid E in 3-dimensional space, then SS, F.…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: Use Stoke's theorem to evaluate f(V × F) · ndS, where F(x, y, z) = (x², y², z²), n is oriented in…

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Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

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Q: Verify Stoke's Theorem. F=, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane.…

A: To verify Stoke's theorem for the below function. F=y,−xz,xz2

Q: Use Stokes' Theorem to evaluate ∫CF⋅dr. In each case C is oriented counterclockwise as viewed from…

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Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: Let G be the solid enclosed by the plane z = y, the xy-plane, and the parabolic cylinder y = 1-x²…

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Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

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Q: 12. Let R be the region of the plane R= {(r, y) : # 2 0 and ²+ y? < 2}. Describe R using polar…

A: Here, the given region is: R=(x,y):x≥0 &amp; x2+y2≤2

Q: Verify Stoke's for F = (2x – y)i – yZ“]-y-zk where S is the upper half of the sphere x2 + y² + z² =…

A: Here verify Stoke’s theorem in the vector F = (2x –y) i – yz2 j – y2z k Where S is the upper half of…

Q: Use Štoke's Theorem to evaluate the line integral - 2ydx +-6zdy + dz where C is the intersect | of…

A: Strokes theorem is ∫CF→.dr→=∫∫S∇×F→.N→dS=∫∫ScurlF→.N→dS x=rcosφy=rsinφ

Q: Calculate S,F.as if F(x,y,z) = xi+ yj and the positive oriented surface o is : The portion of the…

A: To find, ∫∫SF→.dS→ Given that, F→x,y,z=xi^ + yj^   Part i Given portion of plane x+y+z=1 bounded by…

Q: Use Stokes' theorem to evaluate dr. Assume C is oriented counterclockwise as viewed from above. F=…

A: To use the Stokes' theorem to evaluate the line integral.

Q: (a) Let S be the surface z2 = x² + y? bounded between the planes z = 0 and z = 2. Evaluate (z –…

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Q: E is the solid in R3 bounded by the cone surface z = square root (x2+ y2 ) and the plane z = 3, and…

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Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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Q: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

Q: What is the surface area of the portion of the surface z= x?+y that lays over the triangle on xy-…

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Q: Use Stokes' Theorem evaluate 4F.dr if to F(x, y,z)= xzi+ xyj+3xzk and C is the boundary of the…

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Q: Let R be the triangular region of the plane with vertices (0,0), (2, 1), and (1,2). Consider the…

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Q: Let S be the triangular prism with the triangular face in the plane y-3 removed. Let C be the…

A: Given curl F→=xi^-yj^ and the given plane is y=3 So, ϕx,y,z=3j^ Therefore, calculate curl F→·n^ curl…

Q: ntegrate G(x, y, z) = x + y + z over the portion of the plane 2x + 2y + z = 2 that lies in the first…

A: Given information:

Q: Verify Stoke's Theorem for A = 3yî – xzj + yzk, where S is the surface of the paraboloid 2z = x + y?…

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Q: II3. S is the part of the paraboloid z = x² +y² below the plane z = 4 oriented upward and F(x, y, z)…

A: Given the surface

Q: Let F(x, y, z) = -2yi – 3zj – 5xk and C be the circle x? + y? = 9 that forms the boundary of ơ in…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: Use Stokes' Theorem to evaluate  F · dr  where C is oriented counterclockwise as viewed from above.…

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

A: We need to find the surface integral. We will need basic knowledge of parametrization of vector…

Q: b) Use Gauss' theorem to evaluate SS F · ndS where F = (x² – y)i + y°z²j+ (xy – yz³)k and o is the…

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Q: Evaluate the surface integral. x2yz dS, S is the part of the plane z = 1 + 2x + 3y that lies above…

A: We have to evaluate the surface integral x2yzdS, Where S is the part of the plane z=1+2x+3y that…

Q: Use Stokes theorem to evaluate F- dr. where F = (2, 2z, y) and C is the boundary of the paraboloid…

A: Stokes theorem: ∫CF.dr =∫∫Scurl F.N ds Curl F of the vector function F=f1i+f2j+f3k is…

Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Verify Stoke's theorem for F = -2yzi + vj +3xk over the surface defined z = 5- x² -y? above the z=1…

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Q: The wedge cut from the cylinder, x? + y² = 1 by the planes, z = -y and z = 0. Use a tripple integral…

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Q: 1.Find the area of the surface. a. The part of the plane 2x + 5y + z = 10 that lies inside the…

A: Note : As per our guidelines we can supported to answer only first three subparts

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: Find the extreme values of f(x,y,z) = x-yz + 1 on the intersection of the plane z= 3 with the sphere…

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Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk %3D (i) over the surface of the box bounded by the…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.