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- Determine whether the function f:(-1,00) → R defined by f(x) = 3 x+1-e 3 + x is concave or convex. c (a) f: (-1,00)→ R defined by f(x) = 3√√x+1-e-4x + x.Given f(x) = x+1 and g(x)= = cos x, determine the domain of the function f(g(x)).b) Determine the commutator i.e. [θ‚΂] = (΂΂ − ΂΂x)ƒ(xyz) = ?
- Consider the simple functions below, f(x) = x? (1) f(x) = x³ (2) f(x) = x* + 2x3 (3) f(x) = sin(x) (4) f(x) = cos(x) (5) f(x) = e* (6) f(x) = sin(x) + cos(x) (7) f(x) = cos (x) + sin?(x) (8) f(x) = cos(x) +1 (9) f(x) = sin(x) + x (10) (a) Of the ten which function(s) are odd. Indicate them by their equation number and draw a box around your answer. (b) Of the ten which function(s) are neither even nor odd. Indicate them by their equation number and draw a box around your answer.Find an expression for the indicated set, involving A,B,C, and any of the operations u, n, - (subtraction), and '(complement): {x | x is an element of exactly one of the three sets A, B, and C}Use a trial function p = c₁x(a − x) + c₂x²(a − x)² - for a particle in a one-dimensional box. For simplicity, let a= 1, which amounts to measuring all distances in units of a. Use the properties provided in the image to show the results of each value of H and S. Show procedure in a clear way. Do not skip any steps
- Define the term lambda max (λmax)P7F.9 In this problem you will establish the commutation relations, given in eqn 7E. 14, between the operators for the x-, y-, and z-components of angular momentum, which are defined in eqn 7F.13. In order to manipulate the operators correctly it is helpful to imagine that they are acting on some arbitrary function f: it does not matter what fis, and at the end of the proof it is simply removed. Consider [,,1,] = ,-11. Consider the effect of the first term on some arbitrary function fand evaluate A D -x dx se The next step is to multiply out the parentheses, and in doing so care needs to be taken over the order of operations. (b) Repeat the procedure for the other term in the commutator, 1,1, f. (c) Combine the results from (a) and (b) so as to evaluate l f-11f;you should find that many of the terms cancel. Confirm that the final expression you have is indeed iħl_f, where l̟ is given in eqn 7F.13. (d) The definitions in eqn 7E.13 are related to one another byEvaluate the following commutators d (a) | x, dx d (b) | х, dy d (c) dx d + x dx -
- If we have two operators Ậ = x and Ê = d/dx and a function f(x) = x². Clearly indicate if these two operators commute or not?4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx if B and b are constants and real numbers? Show your work in detail.Which of the following statements describe principles or rules you should consider when writing an electron configuration? Select all that apply. Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation... SHOW MORE v a no two electrons can have the same spin in the same orbital b electrons occupy orbitals from higher to lower energy levels electrons should be divided among different orbitals within the same subshell to avoid pairing if possible d electrons occupy orbitals from lower to higher energy levels e paired electrons must have the same spin One more question about sulfur! Which of the following pictures represent orbitals in a sulfur atom in its ground state? Select all that apply. A. В. C. D. Е. B.