Let B = Z[x] denote the set of all polynomials in x. Show that B is denumerable.

Q: xy + xy + xy

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Q: Let ƒ(x, y) = x² + 4y² and let C be the line segment from (0, 0) to (2, 2). You are going to compute…

A: Given: f(x,y)=x2+4y2 We need to find the line integral in two different ways.

Q: 3. 4 f(z) 1 14 20 31 2.

A: Given: The table is as follows:   Introduction: The extreme value theorem states that If f is…

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Q: Find the following commutators by applying the operators to an arbitrary function f(x) [e, x+d²/dx²]…

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Q: f(x + xo) = e' Pxo/h ƒ (x) (where xo is any constant distance). For this reason, §/ħ is called the…

A: The three problems are solved in the steps below.

Q: Let A = Ao sin(ωt − βz)ax Wb/m in free space. (a) Find V and E. (b) Express β in terms of ω, εo, and…

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Q: Find the gradient of the function f(x,y) = 6y-7x at the point (8,10). Then sketch the gradient and…

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Q: In considering two operators that correspond to physical observables, if the operators commute, then…

A: If two operators A and B commute, that is, [A,B]=AB-BA=0, then they share a complete set of…

Q: PROBLEM 2. Find the eigenvalues of a Hermitian operator represented by the following matrix: 1 Â = i…

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Q: If Hn (x) is the nth order Hermite polynomial, then which of the following integrals is equal to 0?…

A: Given: Hn(x) is nth order Hermite polynomial.

Q: (1) Lagrange multiplier is a very useful technique to determine the extremum of a function under…

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Q: s. In a three-dimensional vector space, consider the operator whose matrix, in an orthonormal basis…

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Q: Prove that the expression e*/(1+ e*)² is an even function of x.

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Q: Identify the function as a polynomial, a rational function, an exponential function, a piecewise…

A: Given           f(x) = 7x+2

Q: Sketch f(y) versus y. Show that y is increasing as a function of t for y &lt; 1 and also for y &gt;…

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Q: In discussing the velocity distribution of molecules of an ideal gas, a functionF(x, y, z) =…

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