12. Given the vector field F(x, y, z) = (x² - z²)i + (x + 3z)j + (x² - z)k and S is the surface of the solid bounded by the cylinder x² + y² = 36 and the planes z = -2 and z = 3. Use the Divergence Theorem to evaluate the outward flux of F through the surface S. Show work.

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Q: 66 If a,, b, EN for i = 1,2, 3, then c e determinant; 1+x) a₁b₁ 1+ x) 0₂b₁ (1+x) a₁b₂ (1+x) 0₂b₂…

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Q: If a, b, c are positive real numbers. Then prove that (a + 1)(b + 1) (c + 1)² >77 abct.

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Q: Question 3 ( Consider the differential equation x²y" - 3xy' + 3y = 2x³ – 3x². x³ are = (a) Verify…

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A: DOMAIN -: THE SET OF VALUES OF x WHERE FUNCTION IS DEFINED. RANGE-: THE SET OF VALUES OF f(x)=y WE…

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Q: is equal to Select one: True False L-¹ { = + 3 s² +9 52 - 1 1 -/- 1 + 36 ²1 1 3 { } s² +9

A: Properties of Laplace transformation

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Q: Determine if F(x, y, z)= yz²i+xz²j+ (2xyz-5)k is a conservative vector field. If it is, find a…

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Q: Question 3. If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = 2e5jt…

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Q: A) Find x{(e-51-7)²} L B)[ Use the definition to evaluate the Laplace Transform of the function 2,…

A: FIRSTLY WE USE AN IDENTITY, a-b2=a2+b2-2ab ⇒e-5t-72=e-5t2+72-14e-5t⇒e-5t-72=e-10t+49-14e-5t AND THE…

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A: We draw the graph .

Q: =) x1 + x2 + 2x3 + 2x1 + 3x2 + 6x3 + 3x2 + 4х3 + Х2 — Хз X3 - X1 6x4 = 11 19x4 = 36 15 28 6x4 = -12

A: We solve given system of equations by elimination method.

Q: 17. For the following questions, find a projection matrix P that projects b onto the column sp- of…

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A: Use upper and lower sums to approximate the area of the region using the given number of…

Q: 3 Example 63 Let f(x) = 6 is constant. Then, find sin x -1 рр2 cos x 0 p³ 3 d³ 3 dx 3 [f(x)] at x =…

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Q: 2. Find the mass of the lamina that is the portion of the cone z = √ x² +y² between z = 1 and 2 = 4…

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Q: If y - y = 2x, then prove that 2 ence, show that x² - 1\d²y dx² 27 + X. dx² 1 dy dx = (3y² - 1)³

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Q: Let f-4x²+2y². Use excel or any other software to plot the 7 contour plots for λ=4, 2, 1, 0, -1, -2,…

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A: We find the power series and Radius of convergence.

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Q: Consider the differential equation y' = (y² + 3y + 2) ln(1 + y²). (a) Find the equilibria and…

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Q: be let mal me my and 1(n) be etion, we havre, be non- non-Mang

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Q: Properties of Functions be funcion Show that f: R → R defined by f(x) = x³ + 1 is bijective. follow

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Q: 1. Let p be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively…

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Q: Problem F.1 where x > a, a constant. Use any method to find the GS: 2 y"" (x − a)² y' 1 (x − a)³

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Q: 39 Find the sum of the series sin x + 3 sin 3x +5 sin 5x +...+(2k − 1) sin (2k-1)x

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Q: Compute the volume of the solid bounded by the surfaces x2+y2=17y, z=0 and z=√x2+y².

A: The given problem is to find the volume of the solid bounded by the surfaces x2+y2=17y, z=0 and…