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: Use Stoke's Theorem to evaluate Į F· dr where F (x, y, =) = , and C is the triangle with C vertices…

A: given Fx,y,z=z2,y2,xy ⇒Fx,y,z=z2i^+y2j^+xyk^ and a traingle C with vertices 1,0,0 ,0,1,0 ,0,0,2 to…

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: 3. The point (1, k, 4) lies on the plane [x, y, z] = [1, 2, 0] + s[3, 0, 1] + t[2, −1, 1]. Find the…

A: Given point (1,k,4) is on plane.plane  is

Q: B- Consider the following subsets of real plane R² Determine with graph: 1- Arcwise connected A =…

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Q: Evaluate ff, (F n) dS in the following cases: (a) F = (2y+z, x+z, y − x) and S is the portion of the…

A: (a)

Q: 12. Find the area of the surface generated by rotating the curve y = √√x the y-axis. Do not…

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Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

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Q: -1 15. Determine if span R2. 1

A: A set of vector S is said to be span Rn if every vector of Rn can be written as the linear…

Q: B) Find the value of k so that the line: [x, y, z) = [2, -2, 0] + [3, 5, k] is parallel to the…

A: As per guidelines of Bartleby i am supposed to solve on first part , if you want more solution then…

Q: Advanced Math 4. Let f: S^2 → S^2 be a reflection of the sphere which leaves the plane H = {(x, y,…

A: Given Plane : H =x,y,z100x +239x+11z=0 To find: All great circles which are invariant under f.

Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: f(-2)=3 f'(-2) = 4 g (4) = 5 g (4) = 2 The point (-2,4) lies on the curve in the xy-plane given by…

A: f(-2)=3f'(-2)=4g(4)=5g'(4)=2

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

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Q: Let F(x, y, z) = -3y² + 4z + 6æk and C is the curve of the intersection of the plane x + y + z = 2…

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Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: A) Show that the function u(x; y) = 5x4y - 10 x²y³ + y5 is harmonic and determine the harmonic…

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Q: V = R³. Let W 1 be the xy - plane and let W 2 be the z - zxis : W 1 = {(x, y,0): x, y = R} W2 = {(0,…

A: V=R3  and  W1 be the xy-plane and W2 be the z-zxis defined by             W1={(x,y,0):x,y∈R}…

Q: b) Use Gauss' theorem to evaluate RR F. ndS where F = (x² - y)i + y³z²j + (xy – y²z³)k UTM UTM and o…

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Q: Find the distance from y to the plane in R³ spanned by the set (U₁, U₂} 6 - 2 4 y = -9 a. b. C. 43₁…

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Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

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.