Find the value of the right side of Gauss divergence theorem for F = x²ī+ zī+ yz k over the cube formed by x = ±1, y = ±1, z = ±1.

Q: Find the fay and fyy: f(x, y) = xe" - sin(xy) + x³y

A: fx,y=xey-sinxy+x3y

Q: The function z is defined by z(x, y) = x y-3 y Find A z and dz when x= 3, y= 5, Ax = - 0.04 and A y…

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: verify that (A + B)T = AT + BT

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Q: (@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

A: To explain why the given function is entire, given function is: fz=5z4−6+zcosz−z3ez

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: Find the analytic function f (z)u+iv if u = a (1+cose).

A: We have to find the analytic function

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: if r'y-- 2y + 1.

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Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: 3. Find the derivative of the function f(x, y, z) = xy + yz + zx at the point (1,-1, 2) in the…

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Q: Find the analytic function f(z) = u + iv if u = 2 cos x .cosh 2y cos 2x + cosh 2y

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Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…

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Q: Find m such that the function y= Aex satisfies the equation 2y"=y'+y

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Q: Show that f(x, y) = x2 - y2 is harmonic. Verify the mean-value property for f(x, y) directly [expand…

A: Given that f(x,y)=x2-y2To check:f(x,y) is harmonic harmonic condition:…