Determine the general solution of the differential equation y" + 4y = sin(3t).

Q: Consider the heat equation Ut = AUxx, a €R>⁰, 00 with boundary conditions ux (0, t) = ux (L, t) = 0,…

A: i) In the heat equation the unknown variable is temparature. i,e the heat flows into (respectively,…

Q: Use Theorem 9.17 to give an upper bound to the 30th truncation error for the series 00 n=1 (-1)^ n²…

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Q: . Find the curl of the following vector fields: (a) F = cos(e)i + √y³+y6 + y7j+z¹+tan² z k.

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Q: Solve the given initial-value problem. d²x dt² + 4x = -2 sin(2t) + 3 cos(2t), x(0) = -1, x'(0) =

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Q: Evaluate the following integral. x/4 1/4 SSS 000 sin лx sin 2y sin 4z dy dx dz x/4 1/4 SSS sin xx…

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Q: Discuss the type of singularity (removable, pole and order, essential, branch, cluster, natural…

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Q: Evaluate the limit. 3t2t lim. t→0 t 3 ln(3) - 2 ln (2) X

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Q: Prove by induction: Prove that for all natural numbers k and a that 3((5*2^(2k+1) -1)/3 + a*4^k+1)…

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Q: ctions C: R → Rand S: R → R defined by (x) = Σ n=0 2n (-1)" x ²m (2η)! and S(x) ) = 5(x)C(v) +…

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Q: ving nonlinear system of differential equations: x² - []=[x² 2²50] + y² - 50

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Q: Consider the following. B = {(0, 1, 4), (-1, 1, 4), (-2, 2, 12)}, B' = {(10, 3, -3), (3, 1, -1),…

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Q: sian form a + bi. (1) √2e³π/4 (2) eπi/6 (3) (√3+i)4 Convert the following complex numbers into…

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Q: R^n →R is convex, we write L=H*.  (a) Let H(p) = (1/r)*|p|^r, for 1 < r < ∞. Show L(v) =…

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Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

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Q: 3. Solve the following linear systems. 3x2 = { 2x1 + X2 = + 2x2 (a). (b). 2x1 3x1 3x1 - 5x1 3x1 + x2…

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Q: 2. Use the root test to determine whether the series below converges or diverges. ∞ 2n Σ(1+2n²)n n=1

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Q: 3. Consider the function y = log.(x). A. What function is the inverse of y = log(x)? B. Give exact…

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Q: 13. If n is a square, show that d (n) is odd. 14 TC

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Q: Prove or disprove the following statements: (a) A € R³x3 and A³ - A = 0 imply det(A) = 0. (b) A €…

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Q: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: An investment of ​$41,000 was made by a business club. The investment was split into three parts and…

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Q: 6. Show that the special orthogonal group is compact. SO(n) := {A = O(n)| det A = 1}

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Q: d) -3x+6y=5 x + 2y = 6

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Q: P = D = A = Is A diagonalizable over R? choose 4 -3 5 If possible, find an invertible matrix P so…

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Q: Consider the following. 49 7 -7-y ſªº √√ √¹¯³ ƒ(x, y, z)dzdydx Rewrite this integral as an…

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Q: If P is the solid prism shown in the figure below x -2/3 √²/³ f² f² f(x, y, z) drdydz 2/3 ƒ²/³ ſ² ſ²…

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Q: Write the function in terms of unit step functions and find the Laplace transform f(t) = { 2, -2, 0…

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Q: Suppose that a 2 x 2 matrix A has an eigenvalue 2 with corresponding eigenvector [22] and an…

A: For eigen value  the eigen vector is  and for eigen value  the eigen vector is

Q: 7. Observer Design Consider the system represented in state variable form x = Ax + Bu y = Cx + Du 4…

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Q: Consider the functions C: R → R and S: R → R defined by C(x) = Σ n=0 (-1)" x ² (2n)! and S (x) = 00…

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Q: Consider the heat equation Ut = auxx, a € R⁰, 00 with boundary conditions ur(0, t) = u(L,t) = 0, t>…

A: The heat equation you've presented is a partial differential equation that describes the…

Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace a. Find a nonzero…

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Q: A factory produces baskets at a rate Q = x¹/3y¹/621/6 which it sells for p per item. The inputs x, y…

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Q: clock at the post office has a minute hand that is 1.75m long and an hour hand that is 1.26m long.…

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Q: Use the graph to evaluate the expressions (fog)(1)and (gof)(3). (fog)(1) = O y = f(x) 10 ₹ 8- 6…

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Q: Suppose that the probability of observing |0⟩ in the state |ϕ1⟩ is 1/4 and the probability…

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Q: Use the Laplace Transform to solve the initial value problem. Show all necessary work: y" + 2y' - 3y…

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Q: +++ Match the inequality with the graph. E then give the solution X0 Why did you not shade? x² - 2x…

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Q: ) Recall that C[0, 1] is the vector space of continuous real-valued functions on the interval [0,…

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Q: Determine the solution for each disassembly system. x-y>6 y<-2x+3

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Q: Sketch the region of integration and evaluate the following integral. 3x = {(1,0): 05r54,2505 27}…

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