Oh, I have an idea. The contour I'm integrating over is the line connecting w+h to w. So I believe I can use the ML Estimate to show the limit goes to 0...
Homework Statement
This seems to be just a simple limit problem and I feel like I should know it but I'm just not seeing it.
I have a continuous function f, and a fixed w
I want to show that the limit (as h goes to 0) of the absolute value of:
(1/h)*integral[ f(z)-f(w) ]dz = 0...
You need not do the second u-substitution. Use an integral table to solve it once you have done the first u-substitution. You can google 'integral table' to find one if you don't have one in your book.
Homework Statement
Okay, so we've moved on from talking about R^n to talking about general metric spaces and the differences between the two. We're given that X (a metric space) satisfies the Bolzano-Weierstrass Property and that A and B are disjoint, compact subsets of X. Dist(A,B) is defined...
Homework Statement
let g denote the elliptic arc parametrized by z(t) = 2cost + 3isint, for t between 0 and pi/2 (inclusive).
Evaluate the integral of f(z) = z[sin(pi*z^2) - cos(pi*z^2)] over g.
Homework Equations
If g is determined by the function z mapping from [a,b] to C and...
oh yeah, yeah, now I see. That would be w=sqrt(2)/2 + i*sqrt(2)/2. So now I need to solve w=z^3 -2 = sqrt(2)/2 + i*sqrt(2)/2? Since the original equation is of degree six shouldn't I have six solutions?
The problem says: Find all solutions z of the equation: z^6 - 4z^3 + 4 = i
First I factored the equation into (z^3 -2)^2 = i, set w= z^3 -2 and solved w^2 = i for w_1 = sqrt(i) and w_2 = -sqrt(i). I tried setting z^3 - 2 = sqrt(i) and solving but I get stuck there. I really have no idea how...