Recent content by synapsis

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...

hmm...I don't know. It doesn't say so in the problem. Is that something I should be able to recognize?

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?

hmm...I guess I don't really see what you mean. Is it possible to write +/-sqrt(i) in the form a+bi? I can't figure out how.

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...