The Cartesian product G1 x G2 = (A1 x A2, B1 × B2) of two interval-valued fuzzy graph of G1* and G2* is an interval-valued fuzzy graph of G1* * G2*.

Q: Write down all Laurent series of f(2) Show all the steps of your calculations. = 22-5+6 with center…

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Q: If the equations have no solution, determine the value of k = d) If the equations have infinite…

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Q: 4. Find the Laplace transform of the following functions. a) f(t)=t(sinh t + cosh t)² b) f(t) =…

A: The given functions are ft=tsinht+cosht2 and ft=t2e-4tδt-1   The Laplace transform of sinht is ℒsinh…

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A: Given that Present Price = $ 402000Increased rate = 53%=53100=0.53

Q: prove If f:X→Y is a function and F is a non empty family of subsets of y, then o(f¹(I)) = f¯¹ (o(I))

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Q: Let J,(x) denote the Bessel function of the first kind of order p, and let 2 be a positive real…

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Q: Find the general solution to the following ODE in terms of J, and Y₁. Indicate whether you could use…

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Q: If the equations have no solution, determine the value of k=

A: Given linear equations are 2x+4y+8z=52x+17-ky+7z=72x+4y+12-kz=k+10 The value of k if the equations…

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Q: m* (A) = m (E). For any set A there exists a measurable set E containing A such that

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Q: Let Q(x, y) be the statement " x + y = x - y". If the universe of discourse for both variables…

A: Given statement is  Qx,y :  x+y=x-y   (1)  ∃x∀yQx,y  is False…

Q: Let f: R→ R be a function such that f(x) ≥ x, for all x E R. Show that if Ef (bn) converge, then Σb,…

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Q: What are the A) r₁ = 0, B) r₁=0, C) r₁3, D) T₁ = -1, Fa 0 characteristic roots of a homogeneous LDE…

A: If characteristic roots are ri then solution is of the form ∑cierix and if roots are repeated then…

Q: Duality Exercises Write the dual to the given problems, solve the dual and hence find the solution…

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Q: The graph of f(x) = 6x √(x2 + 2) is shown. (a) Determine x1 and x2 in terms of ε. (b) Determine M,…

A: Given that the graph of                      f(x)=6xx2+2,  and                .

Q: Vectors u and are shown below in black. For each vector projection, select one blue vector from the…

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Q: [6] [1] 4 as a linear combination of the vectors ₁ = 1, V₂ = 2, and v3 = [24] 15 1 5 Express the…

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Q: 4 2 2 3 basis for eigenspace for -1 1-3 that corresponds to λ = 3.

A: Eigen vector equation corresponding to eigen value λ is  A-λIX=0 We have A=423-11-3249 and λ=3

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

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Q: Question 3 The UK government has issued an index-linked gilt on 1.2.2020. The gilt has a coupon rate…

A: Question 3 The UK government has issued an index-linked gilt on 1.2.2020. The gilt has a coupon rate…

Q: agility utility hot diggity

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Q: Let G be a cyclic group of order n, generated by a. Let m be an integer such that gcd(m, n) = 1.…

A: G is a cyclic group of order n.  G = <a>  => order of a, |a| = n.  => an = e, identity…

Q: Let C = {ECR| E or E is countable.} For each E EC, define µ(E) = 1, if E is countable; 0, if E is…

A: As per the question we are given a collection of countable sets C = {E ⊆ ℝ | E or E̅ is countable}…

Q: if the quadratic equation ax2 + bx =c 0 has no real roots then the graph of y= ax^2 +bx+c has A- two…

A: When y = f(x) has an x-intercept at x = a, then we must have           f(a) = 0. i.e., x = a is a…

Q: Let 21, 22 be fixed elements of a Banach space X, and l1, l2 € X'. Define A: X → X by Ax = l₁(x)z₁ +…

A: Given : z1 , z2 are fixed elements of a Banach space X , and l1 , l2 ∈ X'. A : X → X , Ax = l1xz1 +…

Q: Consider the Legendre polynomials of degree n Pn(x) = Σ (-1)m 0<m</ where n is a nonnegative integer…

A: The wrong option is D )

Q: Explain the Matrices of the derivative of a scalar vector (tangent vector) ?

A: Matrix calculus is a specialized notation for doing multivariable calculus.We need to explain the…

Q: Consider the following function: 4x 7x -20 1 -1 -7x 20 7 3 2 -X 11 0 0 0 1 f(x) = When f(x) is…

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Q: Consider the following linear equations: -2x + 6y +9z = -2 -2x + (19 k)y+8z = 0 -2x + 6y + (8 - k)z…

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Q: ind the future values of the ordinary annuities at the given annual rate r compounded as indicated.…

A: Future value of ordinary annuity is  FV=PMT1+in-1i where 'i' is periodic interest rate, and n is…

Q: Use zero-through third-order 2. Taylor series expansions to estimate f(x) = e-x using a base point…

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Q: For a vector z R³ let Tir) be the projection of the vector onto the line that goes through the…

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Q: (2) Test the analyticity of f(z)= = Find the value of Enjti

A: Given information Test the analyticity of fz=ez. Find the value of -11+i.

Q: ind the first five terms in the series solution of y'(x) + (1 + x²)y=sin x, with y(0) = a.

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Q: Let H and K be a subgroups of a group G. Define the relation as follows: a ~ b if and only if a =…

A: here we ahve to prove that the given relation is equivalence relation. for this we ahve to prove…

Q: 3u²-3 u²+4u-5

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Q: Please explain how the recurrence relation simplify.

A: As per the question we are given a recurrence relation and we have to explain how it is simplified…

Q: Let V = R². Show that V is not a real vector space with respect to the following operations of the…

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Q: = Solve the following IVP: (1 + x²)dy + x(1 + 4y²)dx = 0, y(1) = 0

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Q: What is the range of the graph of the quadratic function y= -2(x-3)^2-4

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Q: D 11 10 Q Apply the sorted edges algorithm to the graph above. Give your answer as a list of…

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Q: +y=x, y(0) = 0, y(л) = 0

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Q: 2) u² − au²+ɛ(m+1)(u')" u = 0‚u(0)= 0, u(x) = 1, u'(x) = 0 Obtain an approximate solution for the…

A: As per the question we are given the following nonlinear higher order differential equation : u' -…

Q: f(x)={xcosx1​/x   x≠0​, show thatfis not of bounded variation on[0,π,/2​]

A: To show that a function is not of bounded variation on an interval, we can demonstrate that it has…

Q: Question 2 A family has taken out a mortgage of £350,000 to purchase a house on 1.1.2022. The…

A: P = The total amount of your loan =  £ 350,000…

Q: A principal of $6000 earns 2% per year simple interest. How long will it take for the future value…

A: Given : A principal of $6000 earns 2% per year simple interest.   To find : Time in years it will…

Q: Use Simpson's rule with 4 strips to approximate f₁² √1 + x² dx

A: The given integral ∫121+x2dx. We have to find the value of the integral using the Simpson's rule…

Q: Verify whether the subsets of W of V = R³ is a subspace: (a) Closure Property of Vector Addition W =…

A: The given subset W of V=R3 is W=x, y, z| y=2x, z=0. We have to check whether the subset is a…

Q: n amount of P dollars is borrowed for the given length of time at an annual interest rate of r. Find…

A: Formula for the simple interest is  I=Prt where P is principle amount, r is rate of interest, t is…