Find the flux of the vector field F = (y, z, x) across the part of the plane z = 3 + 4x + y above the rectangle [0, 4] x [0, 5] with upwards orientation.

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Q: Problem #1: Problem #1: Use Stokes' Theorem to evaluate F F dr where F = (x + 7z)i + (3x+y)j +…

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Q: Separation of Variables Sote the separable equation: cosx cosy du se 2=-=-=-* du sin(x) y

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Q: Use linear differential equation method

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Q: Find the volume of the solid bounded by the paraboloids = −9+ 3x² + 3y² and z = 52x²2 - 2y²

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Q: Problem #5: Problem #5: Evaluate the surface integral f with outward orientation. F. ds where F(x,…

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Q: Let y = o(r) be the solution of the initial-value-problem y" + (1+x)y' + (2 ln x)y = 0, y(1) = 2,…

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Q: 13.3. Let y be the curve given by z(t)=t+it², 0≤ t ≤ 2. Evaluate £121²dz.

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Q: Two zeros of P(x) = 5x2(x7 − 14x + 3) are 0. How many other zeros are there?

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Q: Determine the solution of the following differential equation. D6-2D5-2D4-7D³-7D²-4D-4) y = 0 (D7+

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Q: (i) dt — ds Serret Frenet formulae : The arc length derivatives of all fundamental vectors t, n, b…

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Q: (b) Compute the flux of the vector field F(x, y, z) = yi + zk upwards through portion of the cone z…

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Q: (iii) =Tb-kt dn ds

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Q: 1. Consider A function f(x) = x³ - 7x² + 4x + 12. (a) (b) Construct two different fixed point…

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Q: what is the difference between a polynomial and a power series?

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Q: Exercise 5.4.11 Find the matrix for the linear transformation which reflects every vector in R²…

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Q: (Higher Ordered ODE) Determine the solution of the following differential equation. (D³ + D² - 4D-4)…

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Q: Suppose that f(0) possibly be. Answer: f(4) < = 1 and f'(x) ≤ 6 for all values of x. Use the Mean…

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Q: Theorem 1.5. The principal normals at consecutive points of a curve do not intersect unless t = 0

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