Sheet (1) Fourier series -Sketch or graph f(x) which for - -cos² t -π

Q: 5. Consider the polynomial f = X² + X + 8. (a) Determine the roots of f in F5 using brute force.…

A: The given polynomial is .(a) To determine the roots of  in .(b) To determine the roots of in .(c)…

Q: If sec(z) Give exact answers. sin (-7) – cos (1) - tan ¹(²-) - 17 (in Quadrant 2), find

A:

Q: Let n = 13 and let o € S13 be defined by o(1) 12, o (2) = 13, o (3) = 3, σ (6) = 9, o (7) = 5, o(11)…

A: Given the permutation σ in the question:The objective is to determine the order of  and explain why…

Q: The indicated function y₁ is a solution of the given differential equation. Use reduction of order…

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Q: 37. S¹ (√x³ + √/x4) dx 39. ₂₁ |x − 3 | dx - 41. ², (x - 2)x) dx 38. f' (1 + x²)³ dx 40. ²|2x − 1| dx…

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Q: departments have 10, 8 and 7 members, respectively. Each department is to

A: We have to find the total ways.

Q: Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. A1 = 9, x₁ = (1, 0,…

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Q: 8) assume that I is a linear transformation. Find a Standard matrix of T. T: IR ² IR4 where T(e) =…

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Q: Show that lim 1-1 x²-x+1 x+1 1 using the - definition.

A: Given,One has to prove the above expression using  definition.

Q: Q4. a. Solve the linear equation using MATLAB 5x = 3 y 2 z + 10 8y + 4z = 3x + 20 2x+4y-9z=0 1 0 0 1…

A: Solve the linear equation using MATLAB :Objective is to solve this equation by using…

Q: The purpose of this question is to generalize Theorem 3.25 (circulation decomposition, in Chapter…

A: Given: The characteristic vector of a dicycle  is denoted by (a) Let , be a collection of dicycles…

Q: Find the steady periodic solution (1) C cos (ot-a) of the given equation mx" + cx' + kx F(t) with…

A: We have to Find the steady periodic solution xsp(t)

Q: We have considered the case of regular deposits at the end of each month. If deposits are made at…

A: Deposit at the end of each month: Time period:  yearAPR: Balance after  deposits

Q: a) lim (e 1-0 3 ,sec² (2t)) sin²(t)' b) lim i+√8+ti+ sin(at) k In t

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Q: 2. Use the Method of Frobenius to solve xy" + 2y + xy = 0

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Q: - Evaluate f√x+y (y-x)² dxdy using the transformation x+y=ky D.

A:

Q: Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra • Page B:…

A: There are 3 pages; Page A, B, and C.Each page has some links to the other pages of this website and…

Q: 2 = √x²+y²² with cone +2=4 Find the volume between the spheres. draw the shape. x²₁y² +2²=2

A: We need to find the volume between the cone z=√(x^2+y^2) and the sphere x^2+y^2+z^2=4

Q: Let u € C³, v C4, A = uv". Show that rank(A) ≤ 1.

A: This is consequence of one of the famous rank theorems. Theorem:For any two general matrices P and…

Q: Solve it on paper!

A:

Q: When a national sample of heights of kindergarten children was taken, a student was told that he was…

A: Here it is given that when a national sample of heights of kindergarten children was taken, a…

Q: Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4000 to…

A: Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4000 to…

Q: Describe all least-squares solutions of the equation Ax = b. A = 01 b= 2 3 10 The least-squares…

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Q: Evaluate the integral ex+y dA over the domain D defined by x ≥ 5, y ≥ 5, x + y ≤ 13. (Use symbolic…

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Q: se the ordinary annuity formula A=p1+rnnt−1rn to determine the accumulated amount in the annuity.…

A: Formula for the ordinary annuity is where A is the accumulated amount, p is the periodic deposit, r…

Q: Apply the eigenvalue method to find a general solution of the given system. Use a computer system or…

A: Given system of ODE's can be rewrite in following way : where ,Noted that solution is of the form…

Q: annuity if

A: Given thaTime duration is 15 yearAlso $10 invested semiannually

Q: Consider an N x N matrix A  with N orthonormal eigenvectors xi  such that Axi = λi xi  , where the…

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Q: Consider the vector space V defined by V = {(x, y, z) | x+y+z=0}. Let u = (1, -2, 1) and v = (3, -1,…

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Q: gradient of -2 and passes through point (4,-5). Find the intersection point of the straight lines AB…

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Q: Felix is purchasing a brownstone townhouse for $2,600,000. To obtain the mortgage, Felix is required…

A: Felix is purchasing a brownstone townhouse for $2,600,000. To obtain the mortgage, Felix is required…

Q: If cos(z)= Give exact answers. ¹(²7) · 17 19 sin (in Quadrant-III), find

A:

Q: The cross section of a rectangular bar with aspect ratio a has temperature distribution T(x, y, t).…

A: As per the question, we aim to analyze the heat transfer in a two-dimensional rectangular domain…

Q: The two-dimensional Laplace's equation = 0 is, ex²dy² (a) Hyperbolic (b) Parabolic (c) Elliptic (d)…

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Q: According to Newton's Law of Cooling, the temperature u(t) of an object du satisfies the…

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Q: Use Improved Euler's Method to approximate y(2.8) for y'-4x³=0; y(2) =6 Use h=0.2.. Calculate up to…

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Q: Find the maximum and minimum values of the function f(x, y, z)= z³y²z² subject to the constraint a²…

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Q: Problem 3. Consider the cubic polynomial P3(x) = −1+x-2x² + x³, and rewrite it by the following…

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Q: To save for graduate school, a student invests $1470 semiannually in an ordinary annuity with 3%…

A: To save for graduate school, a student invests $1470 semiannually in an ordinary annuity with 3%…

Q: diagonalize the following matrix the real eigen values are given to the right of the matrix لن 3 -3…

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Q: Find the center of mass of the solid S bounded by the paraboloid 2 = Assume the density is constant.…

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Q: Find the general solution of the given higher-order differential equation. y"" + 3y" + 3y' + y = 0…

A: Given differential equation: Objective: To find the general solution of the given higher-order…

Q: Given the following vectors and , find a vector in R4 so that {u, v, w} is linearly independent and…

A: Definition: A set  of a vector space is linearly independent if there are scalars such that .Given:…

Q: log_(2)x+log_(2)(x-6)=4

A:

Q: 7-30 Evaluate the indefinite integral. 7. fx√/1-x² dx 9. f(1-2x) dx 11. (sin(20/3) de 13. sec 3r tan…

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Q: Use a software program or a graphing utility to find the transition matrix from B to B′.B = { (1, 0,…

A: The given Bases are,One has to find the transition matrix using the graphing utility.

Q: What is the cardinality of the power set of a set with 4 elements?

A: Introduction: The cardinality of a set:The cardinality of a set is the total number of unique…

Q: If tan(z) Give exact answers. sin(7) COS OS (²-) = – tan ¹(²-²) - 12 7 (in Quadrant 2), find

A:

Q: What number decreased by 630 equals 1,510?

A: We have to find the number decreased by 630 equals 1,510.

Q: Determine the stability condition for the step size h for the midpoint method, which has the form

A: To determine the stability condition for the step size h in the midpoint method, we need to analyze…