Use separation of variables to solve the following heat equation problem with fixed-temperature boundary conditions: Ut=2U 00 u(0, t) = 0, u(1,t) = 0, t> 0 u(x,0) = 5 sin(ra) - sin(3ra)

Q: Find the center of mass of the solid S bounded by the paraboloid z = 3x² + 3y² and the plane z = 10.…

A: The solution is given by

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Q: Let a, b be constants. Calculate Calculate S √²" (2x + 4y) dx dy. 0 0 Cπ/2 CT/2 [*¹²*¹*² (sin(z) +…

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Q: Use the Steepest Descent method with x) = (0,0,0)' to find a reasonable starting approx- imation to…

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Q: For the following indefinite integral, find the pull Power series centered at x = 0 and then give…

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Here first we have to verify that x1, x2, x3 are the solutions of the given equation. Then using…

Q: Σ (x − 2)n + 1 n = 0 (n + 1)4n + 1

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Q: 1 Prove that the function h(z) = is holomorphic on D1(0) but not holomorphic on D₂(0). (Hint: this…

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Q: Water begins draining from a tank that is filled with water. Let e represent the number of gallons…

A: From the graph each step is 2.For t each step is 2 minitues and for v each step is 2 gallons.So for…

Q: 1. y" + 5y'-6y = 22 +18x - 18x²

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Q: Show that the vectors u₁ = (3, 1,-4), = (3,1, –4), u₂ = (2, 5, 6), and u} = = (1, 4, 8) form a basis…

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Q: 3.) Find the particular solution of y in terms of x to the differential equation that also satisfies…

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Q: Use a numerical solver to obtain a numerical solution curve for the given initial-value problem.…

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Q: Suppose f(x) is continuous and positive for all az except at x = 3, and Select the integrals that…

A: Given that  is continuous and positive for all x except at .Hence f is continuous on   ,so is…

Q: 18 pie is the wrong answer, look at the text box with the red line

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Q: 0, if x < 0 x² if 0 < x < 1. (1-e* if x ≥ 1 Calculate: a. ³₁ x da(x) b. f, a(x) dx c. Check the…

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Q: Use the Maclaurin series cos x = με x9 cos(x9/2) da = 8 Σ /0 n=0 πλη Σ(-1)" . n=0 to approximate the…

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Q: 5. Determine the stability of equilibrium points to the lac operon equation using the method of…

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Q: Suppose F = (y + 2x, 7x + 4z, 6y + 2x) and S is a surface bounded by C, a circle with radius 3,…

A: The given curve is The parameterization of this curve isThe first component make sure that the curve…

Q: Suppose g has a Laurent expansion o -1) ₂²-(-2) ³ as → 0. 9(2) = Σa,2³, j=-1 valid on a punctured…

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Q: ]] F(x, y, z) = zeli + x cos(y)j + xz sin(y) k, S is the hemisphere x2 + y2 + z² = 4, y ≥ 0,…

A: Please repost for other question.

Q: a) 3+6 +9+12 +15= 5) 3-629-12-115= (7-3+6-9 +12-15 = "WIJ !=! IN)"^? (-₁)² = (۱) Hiis odd 1,1 is…

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Q: Figure 2 S

A: As per the guideline, I am supposed to solve only first three subparts of the question from the…

Q: (E). f(x)=0 for VER use the newton Raphson method to evaluate and Approximate values of the…

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Q: 2) Given the following differential equations with output x and input y, linearize the equations…

A: 2)(a) First we have to write the given equation,To linearize the equation we need to perform a…

Q: Find the Laplace Transform F(t)=t^2e^(10t)

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Q: Suppose F = (6y, -4z, 3x) and S is that portion of the plane x + 2y + 3z = 1 that is the first…

A: is the portion of the plane that is in the first octane, oriented counterclockwise and viewed from…

Q: Let M2×2 be the vector space of all real 2 × 2 matrices. Let 1 2 -43-8 B = -1 A = 2 1 04 Let L: M2x2…

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Q: 0, 6) 0, 0) (2,4) (2, 2) ver as an exact or a whole number.)

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Q: 8. Which pairs of graphs in this set are isomorphic? 18 10 11 12 12 25 28 33 35 19 2627 34 国家安网图 20…

A: We hav to find the Graph which are isomprphic

Q: y' = y - y², y(0) = 0.7; y(0.5)

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Q: Write out the spectral factorization of the following matrices: 1 1 0 (c) 1 2 1 0 1 1 (b) (-² −−¹),…

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Q: y = f(x) S y = g(x) base view cross-section The base of a certain solid is the area bounded above by…

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Q: Let a, b be constants. Calculate pln(a) ln (b) S Litace) 0 ex+y dx dy.

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Q: Use Theorem 7.4.2 to evaluate the given Laplace transform. Do not evaluate the convolution integral…

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Q: Use the comparison test to determine if the following integrals converge or diverge. 7 + cos x V√x […

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Q: Torricelli's law states that the rate at which water drains out of a tank through a hole in the…

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Q: Find sin¯¹(x)esin¯¹(x) +1 sin ¹(x)√1-x² [³ -

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Q: P = A a 0 0 Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list…

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Q: What is the equation for the curve of best fit? (-5,-20),(-3,-15),(-1,-10),(1,5),(3,20),(6,35).

A: The given problem is to find the equation for the best fit curve for the given data points.Given…

Q: By using partial sums, determine whether Σ=₁ ln(1 +¹) converges or diverges.

A: The given series .The objective is to determine the converges of the series using the partial sums.

Q: . Does there exist a Möbius Transformation which maps each of the two halflines S+= {z EC: Arg(z) =…

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Q: 10. (§7.6) Solve the following IVP with the Laplace transform. y" - 6y' +9ye³tu(t - 3) y(0) = 0…

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Q: 6. (§7.4) Compute the following Inverse-Laplace transform. 18s L-1 -¹ {(² +9² + ( + + 3)} {√ In (82

A: The Laplace inverse transform, also known as the inverse Laplace transform, is a mathematical…

Q: Use Romberg integration approximation R44 to approximate the following defined integral

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Q: 6. 00 Σ η 2 Say whether the following series converges absolutely, converges conditionally, or…

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Q: the st sub: Z = the + 4x = x²(4t + 3), x(1) = 4.

A: Given differential equationAssume

Q: Find the interest rate needed for the sinking fund to reach the required amount. Assume that the…

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Q: Determine whether the series converges or diverges. OOO Σ n = 1 The series converges by the Limit…

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Q: What is the area of this figure? 7 in 5 in 4 in 5 in 5 in 2 in 2 in 3 in 4 in 6 in 3 in Write your…

A: The composite figure si given.The objective is to find the area of the figure.