# 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. ### Do a integral

\int^{\pi}_{0}Sin(2Cos(\theta))Cos(2n\theta)d\theta I can apply some software to do this integral. However, I need some procedures for this integral. Any help is welcome
4. ### 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
5. ### A pendulum oscillation problem

Homework Statement Consider a pendulum oscillation problem, where pendulum oscillates around the vertical in the downward configuration. Assume that there is no friction at the pivot point around which the pendulum rotates, and assume that there exists a torsional spring that counter acts...