Computations Direction: Find (A U B), (A n B), and A\B of the following sets. Note: R - set of real number and Z+ - set of positive integers. 1. A = {1,2,3} and B = {2,4,6} 2. A = {{a},{a, b}} and B = {{b},{a, b}}| 3. A = {x € Z +|x < 7} and B = {x E Z +\x> 3}

Q: 2y, -Bxy +ry2. B. alues of a, B and y that make this system Hamiltonian. system. and are some…

A: Sol

Q: 24 Let B be a Sx5 matrix and Ca(): A-1)(X--いメ) Let W represent the solution set to the System. Yu Xu…

A: Given that B is a 5×5 matrix and CAλ=λ-1λ2-λ-6λ2+1 Also given that W is a set of solution to the…

Q: For an irreducible polynomial p(X) = 1+X + X² € F[X] consider F4 generated by p(X). Find x1, x2 E F,…

A: Sol

Q: - 3 - 2 Let y = u2 = Find the distance from y to the plane in R' spanned by u, and u2. - 6 u = - 5 1…

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Q: parameter dx2 = e* sin x. Solve the Cauchy-Euler equation x2 dx dy + 4x 3. + 2y = e*. 4. Evaluate L…

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Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: A ball with mass 0,15kg is thrown upward with initial velocity 20 m/s from the roof of a building…

A: Find the maximum height above the ground the ball reaches. The right model is now…

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform cos(t), f(t) = to, 0st 0)

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Q: a) Find the number of walks of length 3 between each distinct pair of vertices. b) There is 1 walk…

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Q: in the parabola 16y = 160- x2. Find the maximum area of the triangle if side s B and C is parallel…

A: Sol

Q: Evaluate t=0.01, Given: 21' + 20I = 100sin(150t) Round-off to 3 decimal places.

A: Given differential equation is2I'+20I=100sin150tI is evaluated at t=0.01 as shown below.

Q: bauk_at fopllof $20,g00 kiļuin the adreed date of fayment. fu fon nall ke pre mecpanical eugineer…

A: #Since the type of interest is not mentioned , taking the interest is compounded annually  The…

Q: 6 9| Find the determinant of 12 7 4 1 3 | 3 191

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Q: Find an orthonormal basis of the plane ¤1+ 6x2 – T3 = 0.

A: Orthonormal basis of the plane

Q: Exercise 94. Evaluate ſcF dr where F(x,y)= xi- yj and C is the line r(t) = (1 -1, t), 0<I<1. If a…

A: Vector field and conservative vector field

Q: Write an equation for the function graphed below. Use the smallest powers possible to meet the…

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Q: Torontiating torm-by-torm givos 02 sin 0<r< L. n odd o weaker series convergence is casily n. and it…

A: Sol

Q: In deciding whether two graphs are isomorphic or not, one can employ the use of a brute force…

A: Sol

Q: Consider the function defined by f(x,y) = 4x² + y? (a) Find the domain and range of f.

A: Given function: fx,y=4x2+y2To find: Domain and range of f.

Q: Solve by D operator method d²y - 2y +y = x²e 3x dy dx2

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Q: Find Vector tangent and normal to at Doint Cl,)

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Q: 8 Given the matrix G = -4 and do =| Then do and d, are G – conjugate if di is given by

A: Conjugacy:  Let G∈ℝn×n be a symmetric and positive definite matrix. We say that the vectors x,…

Q: 1. Solve the Inverse Laplace Transforms 3s + 8 s2 + 2s + 5

A: We have to find the inverse Laplace transform ℒ-13s+8s2+2s+5.

Q: Question 4. Use Taylor's Theorem to estimate sin(3) to within 1/60.

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Q: 1. Solve by D operator method d?y dy -2y +y x2e3% dx2 dx Solvo hu

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Q: dx dx 3. Solve the Cauchy-Euler equation x 4. Evaluate L (sin t - cos t)². 2. dy + 4x dx + 2y = e*.…

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Q: Differentiate the following functions: i. v = 57(12/7+ 3t)

A: We have to differentiate the function v=t57t27+3t .

Q: producf inner Give the definition of the complex space.

A: In this question we have to give the definition of complex inner product space.

Q: 3. f(x) = 4х+5 %3D 9-3х A. x =-1 %3D В. х 3D0 C. x = 3

A: Ques (3) We need to check the continuity and differentiability of f(x)=4x+59-3x at the three given…

Q: 1.21 Decide whether each subset of R3 is linearly dependent or linearly indepe: dent. 4 (b) { | 7 7,…

A: decide whether each subset of R3 is linearly dependent or linearly independent. (a) 1-35 , 224 ,…

Q: 2. Solve the following Cauchy problem: u, + 2ru, - u=a+3ye" with u= 2r - 1 on y=-

A: We have to solve the given Cauchy problem.

Q: Trees Draw a tree on 6 vertices where all but one vertex has degree 1.

A: Given: We have to draw a tree diagram with 6 vertices with 5 vertices of degree 1.

Q: d?y 2y+y = x2e3x dy 1. Solve by D operator method dx2 dx 2. Solve by method

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Q: Consider the folowing inial value problem, (1 - )/" + 3zy/ – 15y - 0, v(0) = 0, v'(0) – 3. Note: For…

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Q: 1) Find the eigenvalues and eigenvector of the given matrix A= Only typed answers are acceptable.…

A: Given matrix is  A = -522-2

Q: Evaluate (107/137). You may assume without proof that 107 and 137 are prime numbers. Show all of…

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Q: a) Find the number of walks of length 3 between each distinct pair of vertices. p) There is 1 walk…

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Q: 2y+y = x²e 3x. d?y thod - dx2 2. Solve by method of variation of parameter - 2 = ex sin x. %3D dx?…

A: Solution by a variation parameter method

Q: Ref for convergent lom to (Xn)neN ) Xx = lim X cL C1), LER. %3D n→め Strow for any sequen ce of…

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Q: Find the general solution of the given system. dx 2x + Зy dt dy = 6x + 5y dt 60°F Sunny e here to…

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Q: A line passes thru (5, 11) and cuts a right triangle with the coordinate axes in the first quadrant…

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Q: Let FECT-2,21], foro. Prave that Max -2

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Q: Find the determinant using Gaussian Elimination Methoc 5w + 6x - 5y + 11z = 7 10w + 36x + 10y – 17z…

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Q: Describe the graph of the equation. r = 2 cos t i - 9 sin t j + k O An ellipse in the plane z = 1,…

A: Equation of an ellipse and center

Q: Find the Maclaurin Series for tan-1(x³). (If not possible to write in Summation Notation, write the…

A: *By Bartleby policy I have to solve only first one as these are all unrelated &amp; lengthy…

Q: m An = {-: m e N}, ne N, where N are non-negative integers. What is lim inf An and lim sup A,? n-00

A: The given set is An=mn: m∈ℕ, n∈ℕ

Q: Dêtermine the equation of the circle graphed below. 10 8. -10 -8 -6 -4 -2 2. 4. 6. 8 10 -2 -4 -8 -10…

A: Given: graph of circle

Q: Describe the graph of the equation. r = 2 cos t i – 9 sin tj + k O An ellipse in the plane z = 1,…

A: We need to describe the graph of the parametric equation: r=2cos t i-9sin t j +k.

Q: eration due to gravity on Earth's surface is g = 9.8 m/s². Let x be the height (in m) measured from…

A: Sol

Q: Calculate ri(t) · r2(t)] and [ri(t) × r2(t)] first by differentiating dt dt the product directly and…

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