Let S denote the following surface: S = {(x, y,z) E R' | x =y-z, 0

Q: A) Find the work done by the force F (r, y) = xy²i – x*j over the r (t) = t'i+t°j, 0st S 1. B)…

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Q: Calculate ff f(x, y, z) ds For Part of the surface x = 2³, where 0 < x, y ≤ 10 ; f(x, y, z) = x s…

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Q: Use the divergence theorem to calculate surface integral F. dS, where F(x, y, z) = x*i – x²z²j +…

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Q: Evaluate the surface integral [/ where F(x, y, z)= xi + yj + z²k and S is the surface parameterized…

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Q: Let z g(x, y) = f(3 cos(xy), y + e#v) provided that f(3,5) = 4, f1(3, 5) = 2, f2(3, 5) = 4. i) Find…

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Q: Let R = {(x, y) E R² | In y <x <1n1< y<e} and let S be the surface defined by the vector function…

A: As per the question we are given a surface S defined by the vector function R(u,v) And we have to…

Q: Let z = g(x, y) = f(3 cos(ry), y+ e") provided that f(3, 5) = 5, fi(3, 5) = 2, f2(3, 5) = 4. %3D %3D…

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Q: . Evaluate the integral: ſf (V · n) da over any surface whose bounding curve is in the (x, y) plane,…

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Q: Let S be the surface bounded by the portions of the unit sphere x2+y2+z2 = 1,the x–y, y–z, and x–z…

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Q: 1 − v2), 0 ≤ u ≤ 2π, v ≥ 0.

A: The surface S is a portion of a paraboloid that opens downwards, truncated at its base. To see this,…

Q: Let S be the portion of the surface z=Vy²+1+e* that lies above the region R= {(x,y)ER?:x²+y?s1,y20}…

A: Given the surface is z=y2+1+ex,and R=x,y∈ℝ2|x2+y2≤1,y≥0. Find I=∬SF·ndσ, where F=ye-x,2ex-2z,y.

Q: Use Stokes's Theorem to evaluate [F.dr where F = (z−y)i + (x−z)j + (x−y)k_and the surface S is…

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Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: be the surfa enned by the vector function R(u, v) (-/- 2u,v + 5, ve¹) all (u, v) € R². Set - up an…

A: Here, in the question given a surface S defined by the vector function: R ⇀(u, v) =(v5-2u, v+5, veu)…

Q: Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0)…

A: Step 1:The surface S given by x2+y2+2z2=1 is an ellipsoid, and we are considering the upper half…

Q: Jse Green's Theorem to evaluate the line integral along the positively oriented closed curve C.…

A: The equation of a straight line joining two points x1, y1 and x2, y2 is given by the formula: y-y1 =…

Q: ) Use Green's Theorem to evaluate the line integral along the given positively oriented curve / F.7,…

A: Here we will find out the required value.

Q: 6. Use the divergence theorem to determine the surface integral of the vector function F on the…

A: The given problem is to evaluate the surface integral of the given vector field over the given…

Q: Evaluate the line integral |(3="y + (1- y):) dz + (z² – z2) dy + z(1 – y) dz where C is any curve…

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Q: Set up and evaluate the surface integral ||(4x+z+6)dS over the surface S ř (u,v)=(v, 4cos u, 4sin u)…

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Q: Use Green's theorem for the work done by the force F= (x - y)i + (x + y)j, for the shaded region R…

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Q: i) Find g1 (0, 4). ii) Find g2 (0, 4). iii) Find the equation of the tangent plane to the surface z…

A: Since g(x, y) = f(3cosxy,y+exy)

Q: Express the rate of inflation from 1985 to 2015 as a percent correct to two decimal places. Year…

A: To find - Express the rate of inflation from 1985 to 2015 as a percent correct to two decimal…

Q: Evaluate the integral for y dx + z²dy + x*dz, where C is the triangular closed path joining the…

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Q: Let F(r, y) = (-y, x² +1) be a vector field and R the region of the plane bounded by the triangle…

A: Given : vector field F→x,y=-y,x2+1 and R is the region of the planebounded by the triangle with…

Q: Use Stokes' Theorem to calculate the line integral of the vector function F = (y, z, x) along the…

A: Given vector function: F=y,z,x The Stokes' theorem is given as: ∫CF→·dr→=∬R∇×F→·n^ds Curl…