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5) dợ = E•dA, where E = (28 V/m?) xy î - (8.3 V/m) sin(2z/n) k, and the area element dA = 0.45 dxdz j - 0.89 dxdy k. Find the expression for dỏ by taking the dot product.
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
Prove the Binomial Theorem, that is Exercises 173 (vi) x+y y for all n e N C) Recall that for all 0rS L is divisible by 8 when n is an odd natural number vii))Show that 2 (vin) Prove Leibniz's Theorem for repeated differentiation of a product: If ande are functions of x, then prove that d (uv) d + +Mat0 for all n e N, where u, and d'a d/v and dy da respectively denote (You will need to...
How do I find i, k, l, m, n, o, p, and q? 5. a. 20.1044 Mass of crucible + cover b. Mass of crucible +cover+unknown 22 . Ч897 22. 4886 NA NA 4.023 16 389 c. Mass of crucible+ cover+ unknown after first heating d. Mass of crucible + cover + unknown after second heating e. Mass of crucible + cover+unknown (after third heating if necessary) f. Mass of crucible +cover + unknown (after fourth heating if necessary) g....
Question A matrix of dimensions m × n (an m-by-n matrix) is an ordered collection of m × n elements. which are called eernents (or components). The elements of an (m × n)-dimensional matrix A are denoted as a,, where 1im and1 S, symbolically, written as, A-a(1,1) S (i.j) S(m, ). Written in the familiar notation: 01,1 am Gm,n A3×3matrix The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively A matrix with the...
Activity: A Journey Through Calculus from A to Z sin(x-1) :- 1) x< h(x) kr2 - 8x + 6. 13x53 Ver-6 – x2 +5, x>3 Consider f'(x), the derivative of the continuous functionſ defined on the closed interval -6,7] except at x 5. A portion of f' is given in the graph above and consists of a semicircle and two line segments. The function (x) is a piecewise defined function given above where k is a constant The function g(x)...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...