# Search results

1. ### This is a asymptotic problem

Homework Statement Find the complete asymptotic expansion of the function \sqrt{1+x^{6}} - x^{3}lnx as x\rightarrow\infty and x\rightarrow0. In each case give the asymptotic sequence in decreasing orders of magnitude. Homework Equations I tried the Taylor Expansion about 0. But I don't...
2. ### Change the integral limit

Homework Statement \int^{2\pi}_{0}cos^{2}(\theta)sin^{2}(\theta)cos(\theta)sin(\theta)d\theta If I set x=cos^{2}(\theta), the integral limit should be from 1 to 0 or need I break this integral into to 4 parts (i.e from 1 to 0 plus from 0 to 1 plus from 1 to 0 plus from 0 to 1)? Homework...
3. ### Cauchy Integral Formula

Thanks, I have worked it out
4. ### Cauchy Integral Formula

Well,thanks. Could you please give a quick explanation of Cauchy Residue Theorem?
5. ### Cauchy Integral Formula

The original problem is this: \oint\frac{(z-a)e^{z}}{(z+a)sinz}dz c=2a centered at z=0 2a<pi we can express the integral around the contour as the sum of the integral around z1 and z2 where the contour is a small circle around each pole. Call these contours C1 around z1 and C2 around z2...
6. ### Cauchy Integral Formula

yes. I have done the form like this: \oint\frac{(z-a)e^{z}}{(z+a)}\frac{dz}{sinz} + \oint\frac{(z-a)e^{z}}{sinz}\frac{dz}{(z+a)} however the first one is not the standard Cauchy Integral Formula
7. ### Cauchy Integral Formula

Homework Statement Using the Cauchy Integral Formula compute the following integrals,where C is a circle of radius 2a centered at z=o, where 2a<pi Homework Equations \oint\frac{(z-a)e^{z}}{(z+a)sinz} The Attempt at a Solution