Using residues, where a > 0 evaluate the integral L²+ 3x sin ax (x²+4)(x² + 16) 8 dx

Q: Find the orders of the following members of S16, and determine which pairs of them are conjugate:…

A: The order of an element of Sn  is the least common multiple of the size of its cycles.(i)  (1  5  7…

Q: Calculate the adjugate Adj(A) of the matrix A= 2 Select one: O 2 1 2 301 4 2 1 3 1 2 1 2 4 4 3 1…

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Q: Write the given system in the matrix form x' = Ax + f. dx -=t³x-y-z+t . = etz - 2 =tx-y+9z-e¹ dy dt…

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Q: Find a general solution to the given differential equation using method of undetermined…

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Q: Fill in the blanks in the following proof. Claim: Let n Proof: Take € = = 1+ for all n € N. Then an…

A: The problem is to proof with the help of definition that the sequence xn=1+1n does not converge to…

Q: Consider a plane curve defined by the parametric equations :  x(t)=acos^3 (t) and  y(t)=asin^3 (t)…

A: The curvature κ(t) of a plane curve defined by parametric equations x(t) and y(t) is given…

Q: and W be vector spaces and A : V → W be a linear map. (b) Let V, W be a pair of vector spaces and A…

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Q: Let --->u =[2,-2,1] and --->v=[-3,5,-1] (a)  COMPUTE the distance between -->u and -->v . (b)…

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Q: X 1+x² List the elements of the requested image or preimage. No set notation needed. Let q be the…

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Q: Suppose you are planning to save money for a future expense. You decide to deposit $500 at the end…

A: Annuity Formula: The future value of an annuity, where payments are made at regular intervals and…

Q: Determine whether the given matrix is diagonalizable; if so, find a matrix E and a diagonal matrix D…

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Q: 4. y"+y = √2 sin √√2 t, y(0) = 10, y'(0) = 0 Ans. y = 10 cost + 2 sint-√√2 sin √√2t

A: The given problem is to find the solution for the given non homogeneous linear differential…

Q: 5. L (s 2 s +2 + 4s+ 5)² e 6s

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Q: True or false: if (n) converges, then every subsequence (n) is Cauchy. Select one: O True O False

A: True or false

Q: (ii) Let W be the subspace of R4 which is spanned by the vectors a₁ = (-1, 1, 2,5), a₂ = (0,…

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Q: In a certain country, area codes have four digits and are subject to the following restrictions. The…

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Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

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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: Use upper and lower sums to approximate the area of the region using the given number of subinterval…

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Q: Which of the following transformations are linear? Select all of the linear transformations. There…

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Q: A linear second-order non-homogeneous equation models this scenario: People falling at a height of…

A: The objective of the question is to represent the given scenario as an initial value problem in…

Q: Figuring a tip: You are having dinner at a burger restaurant. The price of your meal is $24.00 You…

A: You are having dinner at a burger restaurant. The price of your meal is $24.You are tipping 20%…

Q: Determine a mapping of the form (x, y) (_) from y = f(x) for each of the following. y = 3f(2x)…

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Q: (c) Part of the parabola y = 2(x + 1)² from the point (0, 2) to the point (-1,0). (d)…

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Q: If V(x) is the rate of change of the volume of a live band in decibels/m and x is the distance from…

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Q: Given ƒ"(x) = 7x +5 and ƒ'(0) = −2 and ƒ(0) = 1. Find f'(x) and find ƒ(4) =

A: Given,this is the required answer of the given question

Q: 24 A figure is shown. (-2.7) (-2.1) (2.7) (2.1)

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Q: Students are asked to prove the following statement: Theorem: If An B = AUB, then P(AŬB) = P(A). One…

A: The objective of the question is to evaluate the correctness of a student's proof of a theorem in…

Q: Evaluate the derivative of f(x) = (arctan(x))4ª

A: .

Q: Use the contour diagram of f to decide if the specified directional derivative is positive,…

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Q: Exercise 10.4.6 Consider the linear transformation T: P3 → P3 given by T (p(x)) = p(x+1). Find…

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Q: The limit comparison test states: an bn Suppose [an, [bn are series of positive terms and that L =…

A: The objective of this question is to understand and apply the limit comparison test for series…

Q: State the initial value problem describing the mass's motion upon starting from its release,…

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Q: 22. Let G be a group and let H and K be subgroups of G. For a € G, we define the double coset HaK =…

A: We show the equality of the sets by showing one is contained in the other and vice-versa.

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: 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…

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

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Q: A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a…

A: We have to find the position of the mass at any time t. We have to Determine the quasi-frequency and…

Q: Suppose that G = (V, E) is a directed graph. A vertex w E V is called reachable from a vertex v € V…

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Q: (i) Write the following permutations in S9 as a product of disjoint cycles 1 2 3 4 7 298 5 6 7 8 9…

A: Given  f  can be written as a product of disjoint cycles as                 f = (1  7) (3  9  5) (4…

Q: Using the method you described, what are the equilibrium points when m=85 and g=9.8? Please show…

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Q: Fill in the blanks in the following proof. Claim: Let xn = 1 + for all n E N. Then x,, does not…

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Q: For which of the following matrices is [2 21 Ra [1] -41 [121 H an eigenvector with a nonzero…

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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: Find a unit vector in the direction of 54 1 -|2 1 A unit vector in the direction of the given vector…

A: Find a unit vector in the direction of .

Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹t4 c) f(t) = est sin(3t) e)…

A: Recall the formula of Laplace transform: For any non-negative integers L{tn}=n!sn+1 .The property of…

Q: Suppose matrix A is symmetric and has eigenvalues X₁ = 7 and X₂ = 2. The corresponding eigenvectors…

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Q: 24.1. For each of the following relations, answer the following: Is it a function, and if so, what…

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Q: Suppose f is differentiable and f' is increasing on an interval (a, b) (that is, f is concave-u…

A: is differentiable and is increasing on an interval .We have to show that  is convex.

Q: The left Riemann sum is supposed to be 275.02041 but I don't know why? I also got 280.16326.

A: Given:The left Riemann sum is supposed to be 275.02041 but I don't know why? I also got…