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...
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...
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...
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
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