(Section 17.8) Let surface S be the surface of the solid given by - ≤x≤ ≤ y ≤ }, -<*(a) Find the outward flux of F(x, y, z) = (x, 2y, z) through surface S.

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A: In the given question, maximum and minimum values of the function f(x, y, z) = ax + by + cz, where…

Q: arctan dA Xx Calculate where R={(x, y) / x² + y² ≤ 4, x² + y² ≥1, y ≤x≤ 0}

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Q: A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1,…

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Q: Explain the conditions for the origin a node of the system x' = Ax?

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Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: Evaluate fx, fy, fz at the given point: a) f (x, y z) = x³yz² at the point (1, 2, 3)

A: We are solving the first question and for the remaining question post the question again and also…

Q: k) Find a Harmonic Conjugate v(x, y) = _ of u(x,y) = x² -y²

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Q: 4. Find x and y such that =x'y subject to *+*= 36, x20, y20 attains a maximum value. A) (24,12) B)…

A: Given: x+y=36, x≥0, y≥0   ……1   To find: x and y when z=x2y is maximum.

Q: Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,4,0) and (0,0,1). A fluid flows…

A: Given, function is, The rate of flow of the tetrahedron can be calculated by the flux. So, the…

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…

Q: Suppose div(F(-3, -4,3)) = -100. Estimate the flux of ♬ out of a small, outward-oriented box of side…

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A: Note: According to our guideline. We will answer the first question. As the exact one is not…

Q: Find the linearization L(x, y) of the function f(x, y) = (x^3)(y^6) at the point (-2, -2).

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