Use the divergence theorem to compute the flux integral ds where is the outward pointing unit normal vector field to the surface S. S 7=(x³, 3xz², 6y2z) and S is the surface of the solid bounded by the paraboloid z = 4 - x² - y² and the xy-plane.

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Q: 2. Problem 2 Let A = 2 1 -1 1 -3 -1 1 0 1 1 " W = col(A), and x = 3 -4 -1 2 (a) Find Projw(x). (b)…

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Q: Let f(x) = Σ(-1) ¹ n=0 X¹+1 n+1 *(-) for x € (-1,1). Find f' 1 ∞ 2Σxª. Fim² =(- -)- where g(x) = Σ…

A: Recall following infinite series : (1) log⁡(1+x)=x−x2/2+x3/3−x4/4+⋯,|x|<1 (2)…

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Q: (3,-4,-2) Show that 323 f dx + gdy + hdz = f(-3) 12x²y^z²dx + 16y³x³z²dy + 8zy r³dz is independent…

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Q: Solve the inequality and graph the solution set. 4x + 2 6} K++++ -10-9-8-7-6-5-4-3-2-10 1 2 3 4 5 6…

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Q: Consider the complex function f(z)= 1/(z^2 +1)  Find the residue of f(z) at the pole z=i.

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A: Given differential equation isx2y″+xy′+(4x2−4)y=0Rewrite the equation asy″+1xy′+4x2−4x2y=0Let…

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Q: sin 8₂ = ਸ 1²+1 Show that at this stationary value f(r) has a minimum. sin 8₁ = Exercise 1.21 Show…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series co 872 Σ x=0…

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Q: Question 5 Compute SSS √ √ √ ( 2² + y² + 2 ²) dv where T is the solid defined by: x² + y² ≤z≤ √8-x²…

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Q: Use geometric series formula to calculate: 10+50+250+...+10*5^m, where m(greater than or equal to)0

A: geometric series

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Q: dx dt dy = −y − x(x² + y²)¹/2, = x − y(x² + y²)¹/2 dt (a) Show that the system is almost linear in…

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Q: 1. Solve ut = 9ue sin 3x for 0<x<, with u(0, t) = u(x, t) = 0 and the initial conditions u(x, 0) =…

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Q: 2. Let T: P₂ (R) → P₂(R) be defined by T(p)(x) = p(0) + p(1)(x+x²). (a) Prove that T is…

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Q: Question 2 (a) Given the two complex numbers z₁ = 5230° and z₂ = -1 - -√3 j (i) Find z = Z₁ - 2.5 z₂…

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Q: Suppose f(x) = 6x. Determine and graph four distinct antiderivatives of f.

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Q: Use Stokes' theorem to evaluate // V x 7.1 ds where 7 = (9y²z, 3xz, 6x²y²) and S is the paraboloid z…

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Q: foreclosures handled by your firm in each of the months shown.

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Q: Prove that A2 # 0. Let A € M4×4(F) be a diagonalizable matrix with rank 1.

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Q: Find the smallest positive integer k such that 3k = 1 (mod 19).

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