Let w = e®(z+=) dy ^ dz+e" dz ^ dæ + e(z =) dæ A dy be a two-form on R³, and o : (IR>0)² → R³ be the smooth function $(u, v) = (In(uv), In(u+ v), In(uv)). Find o' w. d*w=| |du ^ dv

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A: We have to evaluate by Green's theorem.

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A: We will find out the required solution.

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A: Given functions are 1. f(x, y)=(xy-1)2 3. f(x, y)=(x2-1)(y+2) 4. f(x, y)=x(x2+y2)   To Find: ∂f∂x…

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A: From the graph we can see that, W(2,7) X(5,7) Y(5,1) Z(2,1)

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A: Given: A two-form on ℝ3; ω=e6x+zdy∧dz+e-ydz∧dx+e4x-zdx∧dy. A smooth function, ϕ:ℝ>02→ℝ3 defined…

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A: The direction field is obtained as follows:

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A: Given: F(x,y)=xkeby Formula used: A(x,h)=yn-F(x,y)

Q: calculate..... along the curve in the first octant given by x^2+y^2=1, z=2x

A: Step 1:Step 2:

Q: 2y4 y3 – y2 + y – 1 dy = y² + 2y + In ly – 1| -in ly2 + 1| - y +C

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