3. x'= -2tx + y, y'= 3x-y

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Q: 3. Solve the following boundary value problem =-3₁ +5₂] V₁=₁+₂ 31(0)2, ₂(0)=1

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A: We know Taylors series of f(x) about x=a is  f(x)=∑k=0∞f(k)(a)k!(x-a)k

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Q: het H be a Hilbert space. Consider A, B & BL(H) Prove that || A* || = || A|| and | A²A|| = ||A||²2 =…

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Q: Which of the following satisfies the statement f(x) is O(g(x)) when x5log(x+1) f(x) = +16x²? -5x3…

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Q: Consider the Initial value problem ry' = y + r ln(r); y(1) = 2 (a) Estimate y(1.5) using Euler's…

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Q: 3) Convert the following triple integrals to cylindrical coordinates or spherical coordinates (do…

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Q: Q.2: Find the trigonometric Fourier series of the periodic function f(t), and show if it is odd or…

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Q: Let f(x) = { 3x² + 2, بی کر 2x - 3, if x < 3 if x ≥ 3 be a piecewise function. Evaluate 3 √₁³ f(x)…

A: It is known that: ∫xndx=xn+1n+1+C, where C is the integration constant.

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Q: 17.5(1 + t²) = 4ty(y³ − 1)

A: The given equation is: 51+t2dydt=4tyy3-1 Solve the given differential equation.

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Q: Q4:A/ solve the following linear programming problem using graphical method Max (Z)=80x+72y S. T:…

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Q: 1. Consider the function f(x, y) = {√x² + y² if x # (0,0) 0 if x = (0,0) Evaluate f(x, y) over the…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X₁+2x₂ ≤ 150 3x₁+4x1…

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Q: Show all work. Write each matrix solution as one matrix. 1. Consider the vector valued functions x,…

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Q: /Solve the following linear programming problem using the graphical method Min (Z)= 20X+30Y…

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Q: 7. A banquet hall calculates an 18% tip of the bill before tax for the waitstaff. The waitstaff…

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Q: Evaluate the convolution between h(t)= e2u(t), and x(t)=2u(t).

A: From the above details we have,

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Q: 3. Consider the following matrix 3 1 -1 4 1 1 5 A = 1 a) Show that the matrix A is positive…

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Q: Solve: y" - 3y' - 4y = -8e¹ cos2t Complementary Solution: Yc = C₁eAt + C₂ B eEt Write the letter…

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Q: For the given p-series, identify p and determine whether the series converges. P = . Therefore the…

A: A series of the form ∑n=1∞1np is called p-series p-series converges when p&gt;1 and diverges when…

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Q: The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below.…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1- ل + 27 - +f(x - x) w e dw

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Q: Use a software program or a graphing utility with matrix capabilities to write vas a linear…

A: Consider the given vectors, v=5, 2, -9, 11, 8u1=1, 2, -3, 4, -1u2=1, 2, 0, 2, 1u3=0,1, 1, 1, -4u4=2,…

Q: Problem 5. Are the following metric spaces compact? Prove your claims. (a) The integers Z with d(m,…

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Q: 2. a) Form a partial differential equation by eliminating the arbitrary functions f and g from =…

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A: Given vector is R→x = ∫0π2 sin2x3x+1,   lnx2-1,  xx2+1 dx

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Q: A periodic function ƒ (t) is defined by na f(t) = { di f(t)=ƒ/213< Find the Fourier series…

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Q: etermine the convergence or divergence of ∞ ΣΕ n=1 (−1)n+1 3η

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Q: Problem 2. To prepare for summer, Diffy E. Kew is trying out a new lemonade recipe. Through rigorous…

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Q: Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute…

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Q: √√2 (5 (5x + 3y)dA where R is the parallelogram with vertices (0,0), (2,1), (-1,3), and (1,4). Use…

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Q: Suppose V₁ is a vector of all entries 1 in R" space, which we call "1-vector". What is ||v₁||2 (12…

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Q: Part II: Problem Solving. Solve the following: 1. Consider the linear system a. b. 7x + 7 x 2 = 1…

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Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: 1) Let A be a Banach algebra with unit, Let at A and r(a) <1 Then (1-a) is invertible and (1-a) ² =…

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Q: 3. Apply Lagrange's interpolation formula, find In 9.2 with n=3 and the values below 9.5 10.0 11.0…

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