Write each of the following functions in the form w = u(x,y) + iv(x,y) :
h(z) = (3z + 2i)/(4z^2 + 5)
Find limit:
lim z→2+2i |z^2 − 4| =
Write each of the following functions in the form w = u(x,y) + iv(x,y) : h(z)...
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmonic, find their conjugate har- as functions of 2. 2x2 2лу — 5х — 22. Зл? — 8ху — Зу? + 2у, (а) и(х, у) (b) и(х, у) (с) и(х, у) (d) u(a, y) 2e cos y 3e" sin y, = 3e-* cos y + 5e-" sin y, = elx cos y - e y sin y, (e) u(x,...
(%) = u(x, y) + f 0(4,7) For each of the following functions, write as f(z) = u(x, y) + í v(x, y) and use the Cauchy-Riemann conditions to determine whether they are analytic (and if so, in what domain) a. f(z) = 2 + 1/(2+2) b. f(z) = Re z C. f(x) = e-iz d. f(z) = ez? 16 marks]
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
scalar functions of position, ?(x, y, z) w(x,y.z) be vector functions of position. By writing the subscripted component form. verify the following identities. 5. Let and ?(x,y,z) be and let v(x, y, z) and (b) Div(v +w)- Div v + Div w (c) Div(pv)-(Vp) v+(Div v)
7. Let f:D + C be a complex variable function, write f(x) = u(x, y) +iv(x,y) where z = x +iy. (a) (9 points) (1) Present an equivalent characterization(with u and v involved) for f being analytic on D. (Just write down the theorem, you don't need to prove it.) (2) Let f(z) = (4.x2 + 5x – 4y2 + 3) +i(8xy + 5y – 1). Show that f is an entrie function. (3) For the same f as above,...
given the quadratic form h(x,y,z) = 3x^2 +3xy - 2y^2 + 3xz -4z^2 if a function g(x,y,z) is = h(x+3,y+2,z-5) and has an origin that is a critical point for h(x,y,z) find a critical point for g(x,y,z) while not calculating one, also is it a minimum or a maximum and is it unique?
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z Problem 4 (a) Derive the demand functions for the utility function (b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the...
Is W = {(x, y, z, w) | x − y = 2z + w & w − y = 2x + 3z} a subspace? Justify your answer. If it’s a subspace, find a basis for W and compute dim W.
1. Find 8 different 2-level minimized circuits to realize each of the following functions. 1. F(W,X,Y,Z) = {m (2,4,6,7,12,14,15) 2. G(W,X,Y,Z) = (x + Y' + Z) (X' + Y + Z) W • Using algebraic techniques • Using network conversion