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- u. IF AXB-0 prove that: RH àU sing the rules of B olo gnese algebra Demoreken's theorem, s implify the following. Booleah ex pression to the sim plest form and then draw the logical circle before simplification a fter simpiification an d the truth table (Ā + ē ).(B+ Ĉ ).(A+B +é)c) Corsider the orthonormol basıs {117, 1273, the stote 1 Y>= 174 e*® 12> and the operators and ansuer the follo wing questions : B = 11>2). I. Cololote I. Get the eigen vo lues and cigenvectors of C and B and use this to thot for argue depends on e while does not.
- A triangle in the xy plane is defined with corners at (x, y) = (0,0), (0, 2) and (4, 2). We want to integrate some function f(x, y) over the interior of this triangle. Choosing dx as the inner integral, the required expression to integrate is given by: Select one: o Sro S-o f(x, y) dx dy x=0 2y y=0 O S-o So F(x, y) dæ dy O o S f(x, y) dy dæ O So So F(x, y) dx dy x/2 =0For Problem 8.16, how do I prove the relations and give the correct expressions?How would I be able to sketch the graph in problem 7.36?
- The Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.Consider a finite potential well of depth -Uo. Consider the case -U₁ < E <0. -Uo -a +ab) Given F(x, y, z) = (x³ + cosh z) i+ (2y³ – 3r²y)j – (x² + 4y²z) k. Use Gauss's theorem to calculate //F .n dS where n is the outward unit normal of o, the surface bounded by the planes, x = 0, z = 0 and x + z = 6, and the parabolic cylinder x = 4 – y².
- a. Write down the energy eigenfunctions for a particle in an infinitely deep one- dimensional square well extending from z = -L/2 to z = +L/2 b. Check that they are eigenfunctions of parity operator (that maps z → −z) corresponding to the eigenvalue (-1)n-1, where n labels the energy level.Verify Green’s theorem in the plane for ∮(3x^2 - 8y^2 ) dx + (4y-6xy)dy, where C is the boundary of the region defined by y = , y = x^2 .Q. Derive the relation betueen unit Vectors of Cylindrical and Carterian Coordinates?