(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

w=(PI*(P0-PL)*R^4*epsilon^3*row)/6*mu*L)*(1-1/2*epsilon)

show that this can be obtained using

w=(PI*(P0-PL)*R^4*row)/8*mu*L)*((1-kappa^4)-((1-kappa^2)^2/ln(1/kappa))

by setting kappa equal to 1-epsilon and expanding the expression for w in powers of epsilon. this requires using the Taylor series ln(1-epsilon)=-epsilon-1/2*epsilon^2-1/3*epsilon^3-...

3. The attempt at a solution

so far I have plugged in 1-epsilon for all the kappas, expanded everything and canceled what I could and have ended up with this:

w=(PI*(P0-PL)*R^4*row)/8*mu*L)*epsilon*((-3*x^6+8*x^5-8*x^4+40*x^2-96*x+96)/(3*x^3+4*x^2+6*x+12))

I found an online polynomial long division calculator but I still end up with a jumbled mess. I was wondering if anyone had any ideas or did I make a mistake in the middle somewhere and that is why things aren't turning out nicely. Thanks so much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Need help with complicated algebra for graduate engineering course

**Physics Forums | Science Articles, Homework Help, Discussion**