Determine whether each of these functions from Z to Z is one-to-one. a) f (n) = n − 1 b) f (n) = n² + 1 c) f (n) = n³ d) f (n) = [n/2]

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A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

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A: Solution of the given problem is below...

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A: Yes, it is necessary to get aware of sigma properties . It help mathematics to improve itself.

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A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

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Q: Infinite ransforms: 21. If Fourier transform of f(x) is F(o), prove that the Fourier transform of…

A: Fourier transform of the function

Q: 3. Solve, showing details: y₁ = 4y2 + 5et y2 -V1-20e-t yı(0) = 1, y2(0) = 0

A: Sol

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Q: Which interval notation represents -3 ≤x≤3? 1) [-3,3] 2) (-3,3] 3) [-3,3) 4) (-3,3)

A: Here given  -3≤x≤3

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Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

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Q: The periodic function T(1) obeys T(x+2) = T(x) and |I| 0,n>0 mn= cos(mr) sin(nx)dx □ Σmn Smn²in²n =…

A: Let us calculate a0,a3 b1 b3 values respectively  Then we check the valid prop8of ghee kronecker…

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Q: b) Consider the following LP problem. Minimize z = 2x₁ + x₂ Subject to 3x₁ + x₂ ≥ 3 4x₁ + 3x₂ ≥6 x₁…

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Q: For items 13, 14, and 15, consider the region R bounded by y = Arctan x, r = 1, and the x-axis.…

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Q: Determine the definiteness of the following constrained quadratics: a) Q(x₁, x₂) = x² + 2x₁x2x2,…

A: Please see the attachment  According to the guidelines we are supposed to do one problem

Q: dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

A: Solution

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Q: 3. Which of the following equations is (are) true? 1 I. | 254 = Arctan (5) + x² 25 O I only O II…

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Q: Find an integrating factor and solve the given equation. 18y dy (18x + 7) + (6²² +15v ) = 0 X dx

A: The given differential equation is                  18x+7y+6x2y+18yxdydx=0

Q: f(x, y) = x² + y² – 14x - 12y – 3. - - a) Determine the domain of f. b) Find and draw level curves…

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Q: Let R be the region bounded by y=x², x=1, and y=0. Use the shell method to find the volume of the…

A: The region R is bounded by the graph of y=x2, x=1 and y=0. Find the intersection of the parabola…

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Q: Advanced Math solve system of differential equations by laplace G-V=3 y+v=-X² u(0)=0 v(0)=1

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Q: 19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which…

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Q: b) Consider the following Linear Programming (LP) problem: Maximize z = 3x₁ + 2x2 Subject to 2x₁ +…

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Q: a) After using the ansatz u(x, t) = X(z)T(t), which equations do you get? Pick only two. (below C'…

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Q: 4- Solve the following differential equation: (1 + x²)dy + (y − tan−¹(x)) dx = 0 -

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