Given Show that the Fourier series for f(x) is π² f(x)= +2 6 (-1) n² n=1 -^≤x≤0 0≤x≤T 2 Σ(-1*¹. (−1)n+1 + ren (–1)" – 1}}sinnx πης n=1 f(x) = {0, (x², cos nx +

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Q: i. It is true when the hypothesis is true and the conclusion is also true. ii. It is true when any…

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Q: Which of the following matrices are singular? a) 2 -1 b) 3 A= 0 -1 4 B= 6 3 2 d) D= 24 10 3 -1 2 -1…

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Q: Example 8.1. Given that 1.0 1.1 y: 7.989 8.403 dy find and dx (a) x = 1.1 (b)x= 1.6. d'y at dx² 1.2…

A: We need to make difference table to solve this problem. Please find step by step solution below:

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Q: Decode the number using the given private key. Decode the number M = 15 using the private key d = 53…

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Q: (a) Determine whether the permutation 42135 of the set {1, 2, 3, 4, 5} is even or odd. (b) Find all…

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A: Find the general solution of each of  partial differential equations  9uxx - 21uxy + 49uyy = 0

Q: Use the binomial theorem to expand and simplify (write out the Sigma Notation first) (5x³ - 3y²)¹

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A: Given PDE is ∂u∂y + c∂u∂x = 0

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Q: values of (1, Ar) on the manifold where (1, B1): Let A and B be Hermitian operators on a real…

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Q: Problem No.2 Evaluate the determinant of the given matrix A= 1 3 4 -1 1 1 -1 4 2 0 1 -1 2 -1 3 2

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Q: Solve the initial value problem dy/dx = (xy + 3x - y - 3) / (xy - 2x + 4y - 8), y(-3) = -2

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Q: lim f(x) = x→3+ Is f concave up or concave down on 1 < x < 3? What is the absolute minimum of f(x)…

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Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: 3. Quadrature: (a) Use two point Gauss-Legendre quadrature to approximate cos(2²) dr.

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Q: Let f(x) = x² + 2x - 1 and g(x) = 2x - 4. Find 3f(x) - 2g(x). 2x² - 2x - 14 3x² + 2x + 5 Option 1…

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Q: Transform: F(s) = (s+2)(s−1)(s−2) O f(t) = −e-² – 3c′ – 4e²¹ 21 O f(t) = c-²¹ - 3e O f(t) = −e²¹ –…

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Q: The set of rational numbers is an ideal of the set of real numbers.

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Q: Define the linear transformation T: R → Rm by T(v) = Av. Find the dimensions of R" and Rm. -1 A = -1…

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Q: Given the discrete metric space for n € Na the discrete metric o defined by the distance function…

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Q: Solve the following system using elementary row operations on the augmented matrix: x1 + x2 + 2x3 =…

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Q: Find the eigenvalues of A, and find a basis for each eigenspace. 63 A-[$] = Select one: A.6-3i, 3₁…

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Q: 3. Convolution Find the Laplace transform. T Jo So e− (t − z)®sin (3t)dt е

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Q: is a solution to the ODE a. x²y" - y = 0; b. x²y" + 6xy' + 4y = 0. Find the values of m for which…

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Q: 42-311 Solve this assignment Problem? 1 2 3 2 3 Ч S 2 1 10 10 5 5 5 5 5 15

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Q: Given the family C[0, 1] of continuous functions ƒ : [0, 1] → R, and the norm ||f|| = sup f(x)]. x=…

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Q: Example 7.16. Given the table x: 310 320 330 log x: 2.49136 2.50515 2.51851 find the value of log…

A: Taking the origin at x0 =330 and h = 10, we have p = (x-330)/10.

Q: Consider A= (0, 4, 2), B =, (6,-1,0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

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Q: Let C₁ be the circle r = 3 cos 0 and C₂ the cardioid r = 1 + cos 0. O (a) Find all point(s) of…

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