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- show that f(z)=(z-1) cos(1/z+2) has an essential singularity at z=-25) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a square with sides of length 1 mm. Calculate the potential differences (in mV) VAB, VBA, VAC, VCA, VAD, VDA, VBC, VCB, VBD, VDB, VCD, VDC between the points in a uniform electric field of 3 V/m parallel to the two sides (and perpendicular to the other two) of the square. (Show your work)Evaluate ∫_0^(π⁄2) ∫_0^1 ∫_0^2 zdz r^2 dr sin u du
- 1. Solve by Cramer’s rule 3x + y + 4z = 11 4x – 4y + 6z = 11 6x – 6y = 3 2. Find the volume of tetrahedron given the following (1, 0, 1), (0, 1, 0), (0, 0, 1), and (1, 1, 1).What are the equilibrium solutions of the DE dy/dt=4ty−t?If there is more than one, list all of them, separated by commas. If none exist, type DNE.Let, w = (xy)/z and x = 2s + t, y = st, z = 2s - t Find (photo attached):
- Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident roots?Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2, y=1 ydx-xdy=7y3dy2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] , where Ĥ is a 1D Hamiltonian with V̂=V0 (constant) (d) [Â,B̂], where  = d^2/dx^2 + x and = 1