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: Using spherical coordinates, determine the volume of the solid that is above the z=2√3 plane and…

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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: 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: 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 D be the triangular region in the uv-plane with vertices (0, 1), (4, 1), (1, 3) and let G(u, v)…

A: Given :-  Let D be the triangular region in the u-v plane with vertices  0, 1 ,  4 , 1 ,  1, 3. Let…

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: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

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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: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

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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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.