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1. ### Evaluate infinite sum using Parseval's theorem (Fourier series)

Homework Statement Show that: \sum_{n=1}^{\infty}\frac{1}{n^4} = \frac{π^4}{90} Hint: Use Parseval's theorem Homework Equations Parseval's theorem: \frac{1}{\pi}\int_{-\pi}^{\pi} |f(x)|^2dx = \frac{a_0^2}{2}+\sum_{n=1}^{\infty}(a_n^2+b_n^2) The Attempt at a Solution I've been trying to solve...
2. ### Find centroid of region - triple integrals, need help please!

Homework Statement Find the centroid x,y,z of the region R cut out of the region 0<=z<=5sqrt(x2+y2) by the cylinder x2+y2=2x. Homework Equations x2+y2 = r2 x= rcosθ y= rsinθ The Attempt at a Solution Centroid x being Mx/m I'm guessing I've been working on this problem...
3. ### Motion in curves - Find radial and circumferential components of V and A

Homework Statement At time t, a comet has the position R = (t2-1)i + 2tj At t = 2, find the radial and circumferential components of velocity and acceleration Homework Equations Vr = V * Ur Vθ = V * Uθ ar = a * Ur aθ = a * Uθ Ur = cosθ i + sinθ j Uθ = -sinθ i + cosθ j...
4. ### DC Circuit problem

Homework Statement Find a) the potential difference between points a and b b) the current of the 20 ohm resistor I drew the diagram in MS Paint. Should be good enough. http://img188.imageshack.us/img188/6515/circuitf.jpg [Broken] 2. The attempt at a solution I just don't know where to...