Evaluate the commutator [d/dx,x2], considering:     (a) an arbitrary function f(x).     b) f(x)=x3-3

Q: Which of the following functions f has a removable discontinuity at a? If the discontinuity is…

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Q: Plot the graphs of f(x) = x^2 and y(x) = √(4-x^2), where x [-2; 2]. Calculate analytically the…

A: The objective of the question is to plot the graphs of the functions f(x) = x^2 and y(x) =…

Q: Q1: Find the gradient of the following function: f(x, y, z) = e* sin(y) In(z)

A: Given Function = f x,y,z = ex siny ln z

Q: Consider the line element of the sphere of radius a: ds2 = a2(dθ2 + sin2 θ dØ2 ). The only…

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Q: Given u x v = (3,-4,-3), find (ü - 3) × (u + 2u). X

A: The cross product of two vectors is given asNote:The cross-product of vector with itself is zero,…

Q: Find the principal invariants, principal values and principal directions of the order tensor T,…

A: The tensor given in the question is  T=3-10-130001 This is a symmetric tensor. TT=T Let us calculate…

Q: f(x) = cos(10(x - 1)), xo = 1, x = 2, n = 2. Find the error estimate for Taylor polynomial…

A: Solution: Let us calculate the nth derivative of the given function.…

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

A: Given Data:The first commutator is [ex,x+d2dx2]And the second commutator is [x3−ddx,x+d2dx2]The…

Q: Suppose that you have the functional J (a) = S². ƒ {y(a, x), y' (a, x); x}dx where y (a, x) = 3x – a…

A: Given, Jα=∫-π2π2fyα,x,y'α,x;xdxyα,x=3x-αcos2xTherefore,y'α,x=3+αsin2x

Q: Determine the following indefinite integral up to a constant c: ∫(sin(3?+7)+cos(7?+3))?? Select…

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Q: If  and B are two vectors that commute with Ô, prove the useful identity (Ô· Â)(Ô · B) = · B+ iÔ(Â…

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Q: In the following function evaluations f(xA), assume the numbers xA are correctly rounded to the…

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Q: Find the partial derivative of the x component of the given function: -x(x2+y2+z2)-3/2

A: Given, The function fx,y,z=-xx2+y2+z2-32

Q: Problem 2: Random variable X has the following pmf and Y = eX. Calculate EY] directly (without first…

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Q: Given [yth, y²] + = 27¹², i 2 [μ²] = 0μv where is the mostly positive Minkowski metric and are the…

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Q: Give the square matrix -6 1 A = 0. The eigenvalues of A are:

A: The given matrix is,

Q: Ex4@Express w = (x-1) ay in the cylindrical coordinates (b) transform F = P cosa ap in the Cartizian…

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Q: Find the gradient of following scalar function: 5x'-7y'+3=* r = V

A: The solution is given in the next image :

Q: Suppose that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?

A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ

Q: the eigenvalues of the following matrix: /2 2 0 220 0 0 A) 0, 1,4 B) 1.2.2 C) 5,0,0 D) 5, 5,0 E) 0,…

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Q: The eigenvalues a

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Q: Given a function : y(t) = A sin(kx-wt) Prove that: d^2 y / dt^2 = - w^2 y(t) Where A, k, x, w are…

A: Given function is, yt=Asinkx-ωt

Q: Find a scalar potential, fi, if  F=(3x^2yz^2)i+(x^3z^2)j+(2x^3yz)k, and fi(1,1,1)=1

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Q: Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there…

A: Let’s consider the following sets of vectors,

Q: Calculate the first derivative of the function f(x) = 2x e -X at the point x=1.19. Express the…

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Q: 19. Inz (Use 0 <0 < 2π.)

A: Here let us consider a complex function fz where z is represented as,  z=x+iyx is the real part and…

Q: The figures below are graphs of r(u, v) = ui + sin u cos vj + sin u sin vk, where 0 ≤ u S/2 and 0 S…

A: given graph for r(u,v).

Q: A curve in three dimensional space is parametrized as 7(u) = cos(u)i + sin(u)j + cos(3u)k, + COS u e…

A: Given, r→u=cosui^+sinuj^+cos3uk^