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1. Determine the largest domain Ω on which the function f(z) = log z / z is analytic, where log z is the principal branch of the logarithm. Furthermore, compute f'(z) on your domain Ω.
If u(x, y) = (1/2) ln(x2 + y2) and v(x, y) = tan-1 y/x, then is f(x + iy) = u(x, y) + iv(x, y) analytic on Ω, where Ω is the complex plane with the point z = 0 removed?
To determine whether the system described is a group. G = set of all integers, a.b = a - b
Let P : C -> R be defined by P(z) = Re z; show that P is an open map but it is not a closed map. ( Hint: Consider the set F = { z : Imz = ( Re z)^-1 and Re z doesn't equal to 0}.) Please explain every step and justify.
find all solutions to the following equation on the interval 02picos2 cosx
Find the area S of the region bounded by the parabola y = 3x2, the tangent line to this parabola at (4, 48), and the x-axis.
A 1976 study of women smokers over 30 years of age who delivered premature babies (fewer than 260 days of gestation) reported an infant survival percentage of 72%. Suppose researchers would like to estimate the current survival proportion. Using the..
Problem 1: Simplify the expression (xΛ(yΛz)) V[x'V((xΛy) Λz')]
suppose cotx -6.5 and sinxlt0. find the following quantities you can use .5 instead of a square root in a numerical
Write a simplified expression for the weekly revenue and Construct a table of values and graph the function
For the normal distribtion, the mean plus and minus 1.96 standard deviation will include what percent of the observations? What is the formula to calculate the percentage?
A trapezoid with bases 2 m and 6 m is partially submerged vertically in water so that the top is 2 m above the surface and the bottom is 2 m below the surface.Express the hydrostatic force against one side of the plate as an integral and evaluate it...
Calculate the expected monthly laptop computer sales volumes for Dell and HP at these sites. Calculate the standard deviations of the monthly laptop computer sales volumes for Dell and HP at these sites.
radius of earth 6370 kmmean ocean depth 3800height of biosphere 14kmif the earth were scaled down to a 1m diameter
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