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- a. Use the Cartesian representation L₂ = 1/(x2-17 - 1²/²7) y i ду дх to show that (x + iy)m is an eigenfunction of Îz.Q3: Simplify the logic function F using Karnaugh map? F= ab + ač + abd + ābd + bcd + bcd + ābcd + abcd + ābcd Q4: Simplify the logic function E using Boolean algebra? E= (a bē)b + abc + ābc + āc + bē + bcWhat are the indices (Miller indices) of a plane whose intercepts with three axes are 2,4,2, respectively (121) .a O (212) .b (424) .CO (one hundred and one) .d O
- 5. Identify which of the following functions are eigen functions of the operator d/dx: a. eikor b. cos kx c. k d. kxGeneralizing the Product Rule The Derivative Product Rule gives the formula dv du dr dx (uv) = u- dx for the derivative of the product uv of two differentiable functions of x. a. What is the analogous formula for the derivative of the prod- uct uvw of three differentiable functions of x? b. What is the formula for the derivative of the product uj uz uz u4 of four differentiable functions of x? c. What is the formula for the derivative of a product uj Uz uz* Un of a finite number n of differentiable functions of x?1. Write a boolean function with three variables and it should involve (+) and (.) 2. Draw the table of this function. 3. Draw the shape of this function (like a circuit). 4. Find the Not of the function. (f') , not(f)
- Consider the following LP. (Primal problem) Min 24x1 -12x2 + 4x3 s.t. 3x1 - 3x2 2 3 4x1 + 2x2 + X3 2 1 X1 2 0, x2 s 0, x3 2 0 Let y; be the dual variable corresponding to constraint i in the primal problem. What are the sign restrictions on dual variables y, and y2? a. y1 s 0, y2 2 0 Ob. y1 2 0, y2 2 0 O Cy, s 0, y2 s 0 y1 2 0, y2 < 0 е. None of theseWrite a Boolean expression for the output, Q, in terms of the inputs A, B, and C.Elliptical cylindrical (EC) coordinates are defined by the variables u, v and z, with aconstant a, in terms of Cartesian coordinates as follows:x = a cosh u cos v ;y = a sinh u sin v ; (75)z = z .a. Find the EC metric.b. Describe surfaces of constant u, v and z for various values of the constant a.c. Find the EC basis vectors for arbitrary a.d. Make vector field plots of the EC basis vectors in the x-y plane.e. Find the incremental area and volume expressions.f. Express the gradient, divergence, curl and Laplacian operators in EC coordinates.
- e-ikx and f (x) I give you a function called Q(£, p) and tell you the rules are: î = x, and p = -iħ-. Simply plug in the function Q and Let us play a game. I give you two functions. Let g(x) = e-ax? follow the standard rules of calculus! Work out the following operations on the specified functions. a) £?g(x) b) p²f(x) c) pg(x) d) pf(x) e) &ôg(x) f) Pâg(x) h) &pƒ(x) i) p&ƒ (x) k) Is it true that the operation of âp on a function is always equal to pâ? Justify your answer.I am am doing problem 5. from Serway and Vuille - 11th edition. I dont understand why they use sin 30 and not cos 30 when the fomula for work = (F cos (theta)). d. Is there away way you could draw a diagram to help explain it to me? cheers.4 1. Consider the matrix operator A -2 4 2. a. Show that 3 is one of its eigenvalues. b. Find the other two eigenvalues. 225