Using residues, where a > 0 evaluate the integral x sin ax cos ax x² +9 dx

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

A: Given differential equation: We have to determine the general solution of the given differential…

Q: 8. Express the following linear systems (from) in the form of matrix equations. { (a). (b). 21 2x1…

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Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: A car driver makes a journey in a straight line from A to B, starting from rest. The speed of the…

A: By Bartleby guidline I am solving only first question.

Q: Exercises 12. 1. Compute lim 1 (n!)¹/n (Hint: let Sn = in Theorem 12.3 and recall that lim (1+1)" =…

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Q: Suppose a system of constant coefficient differential equations - Az has a 2 x 2 matrix A with Find…

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Q: Use Newton's method to approximate a root of the equation 3x³ + 6x + 2 = 0 as follows. Let x₁ = -2…

A: Given equation isInitial approximation is We have to find second and third approximation.We know…

Q: Exercise 10.1.2 Consider the following functions T: R³ → R2. For each function T, show that T is a…

A: The given functions,(c) (d) The aim is to show that the map  is a linear transformation and matrix…

Q: Perform the matrix operation. Let A = [22] -8-8 O 4 -3] -16-4 0-3 (0-12] -3 0-12 and B = Find A - B.

A: and To find: .

Q: 2x-3y+z=6 2y + 4z = 12 x-y+2z=1

A: The system of linear equationsto solve for x, y, and z.

Q: ty"-ty' + y = 2, y(0) = 2, y'(0) = -4

A: Given the DE .We will use the following formulas after applying the Laplace transformation.

Q: An electronics store receives a shipment of 30 graphing calculators, including 7 that are defective.…

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Q: Find a unit vector in the direction of the given vector. 80 - 150 A unit vector in the direction of…

A: The given problem is to find the unit vector in the direction of given vector.Given vector

Q: Let A =[1 -1]            [2 0] and --->x =[ i]                  [1 + i] . SHOW that Re (A--->x )…

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Q: Let X be Hausdorff and f : X → X be a continuous function. Show that {x : f (x) = x} is closed in X.

A: Let, .We show  is open and so F is closed.

Q: Find the change of basis matrix [B] & C° ·={[4]·[4]} = {[1]·D]} C 4 B

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Q: 3. Show that Z10 is isomorphic to Z2 × Z5, but that Zg is not isomorphic to Z₂ × Z4.

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Q: Solve the given differential equation subject to the indicated conditions. y" - 2y + 2y = 0, y(π/2)…

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Q: Find the kernels and images of the following homomorphisms. Which of the homomorphisms are…

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Q: Are the two linear transformations the same? No ◆ • S: rotate 45° clockwise about the origin,…

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Q: 4. (4 points) Given that tan (0) and cos(0) > 0, find sin(20) and cos(20). = 1 3⁹

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Q: f(x) = sinx and a) Im (fog) = [0,1] 1) (gof) is periodic with period 2.11 c) Im (fog) = [-1,1] g(x)…

A: f(x) = sin(x) g(x) = M(x) (mantissa function) , it is also                                 known as…

Q: Problem 5. Prove that the space X is Hausdorff if and only if the set ▲ = {(x,x) : x ¤ X} is closed…

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Q: When a 4 kg mass is attached to a spring whose constant is 100 N/m, it comes to rest in the…

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Q: 1) Come up with a 2 x 2 contingency table for which p₁=P2, and for which the row and column totals…

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Q: Let B = {b₁,b₂} and C = = {C₁, C₂}. Find [v] and [v]. 98 6+ 10 [v]. [v] 8 9 -8 -7 -6 = b2 c2 bl Lo…

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Q: Let S be the rectangle in the plane y + z = 1 which has corners at (0, 0, 1), (1, 0, 1), (1,1,0),…

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Q: Let f f(x)dx = 8 and f(f(x))²dx = 9. Find the following integrals: So cf(z)dz = f(f(x))²dx − (f…

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Q: Use the Laplace transform to solve the given initial-value problem. 0, 0≤t< π y" + y = f(t), y(0) =…

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Q: 5. L (s 2 s +2 + 4s+ 5)² e 6s

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Q: 3. Let x = (x₁, x2), y = (y₁, y2) E R². Determine the values of k E R for which (x, y) = x1y1 = x1y₁…

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Q: Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D…

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Q: b) L[4t +5te* +sinh(5)]=

A: We need to find

Q: #3: A 70 lb weight stretches a spring 10 feet. The weight hangs vertically from the spring and a…

A: We are given the following information:Weight of springDisplacement of springDamping forceWeight is…

Q: If ||u||²+||v||²=||u+v||², then u and v are orthogonal.

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: Exercise 10.4.2 Let B = in R². Find [x]B. -1 MGA 0 2 be a basis of R3 and let x = 41 -1 be a vector

A: Goven that  be the basis of  and

Q: Find a basis {b₁,b2,...} for the eigenspace corresponding to (the eigenvalue) X. -25 -15 -9 27 17 9…

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Q: b. An infinitely long string with zero initial displacement is subject to the initial velocity 0, if…

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Q: Prove or disprove: Q/Z is isomorphic to Q

A: Group isomorphism

Q: c) d² y dt² +2 dy dt + y = 4t, y(0) = 0, y'(0)=5

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Q: 370 The marginal profit function for a company is given by P'(x) = √x - 5. Estimate the change in…

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Q: Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state…

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Q: A=[pi 0 0 0][0 pi 0 0][0 0 pi 0][154 0 0 pi] find the eigenvalues of A

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Q: Exercise 10.4.4 Let T: R² R² be a linear transformation defined by T ([%])=[a+b]. Consider the two…

A: The given linear transformation .The two bases  and .The aim is to find the matrix  of .

Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

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Q: Compute the flux of the vector field F(x, y, z) = (2,0, x³) across the portion of the plane x-z = 0,…

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Q: Can you answer these four questions, please?    Find the equation of the line joining the points…

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Q: Let f, g: R → R be continuous at a point c, and let h(x) = sup{f(x), g(x)} for x € R. Show that h(x)…

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Q: A law firm has six senior and four junior partners. A committee of three partners is selected at…

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Q: why can we define P(x)= (2pi) / |f'(x)|? What steps?

A: The expression  is related to the period of a periodic function, such as g(x)=sin(f(x)) or…