TEANUCOGl b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz = 0. he

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A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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A: We first differentiate the given function with respect to x twice. Then y and z will be treated as…

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A: For a function in several variables, partial derivative with respect to one variable say x can be…

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: af Find of f (x, y) = sin %3D dx 1+ Y COS 1+y () Option 1 sin 1+ y 1+ y Ontion 4

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A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: a) Lollowng use Euler ncthoel tsoule The d = yx2-Y for メ=2 at h=o.Ś , h=0.25 y= x +zy h=ol y (2)= }

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Q: 3zyz f(x, y, z) = e %3D fz fy = f =

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

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Q: Let v(x, y) = cos(4x) sinh(4y). Find f(2)with Im(f(z)) = v(x, y).

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Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

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Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y).

A: using CR equation we get....

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Q: D. Find Az) = u(x, y) + iv(x, y) with u as given. Check for analyticity. (a) u= x/(x² + y³)

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

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