Recent content by Geekchick

Try rewriting the problem ie. Look at it as having 2 red, 2 blue, 2 yellow, 2 green, 2 purple, 2 orange, 2 violet, 2 pink, 2 black, and 2 white balls. Then given the twenty balls you are trying to make lines of eight without replacement. Thus the probability you're looking for is the probability...

sin instead of cos but yes. my instructions are to convert to Cartesian and then evaluate. But I'm not sure what the integral will be and with what bounds once I convert it...evaluating should be easy.

Can I work backwards from the definition \intf(x,y)dxdy = \intf(rcos\vartheta,rsin\vartheta)rdrd\vartheta and then I can say rdrd\vartheta=dA and so all I have is \int\intsinydxdy? And I'm terrible at bounds so where do I start there?

Homework Statement \int\int(rsin2\vartheta)drd\vartheta sorry i don't see how to put the bounds in but they are 0<\vartheta<\pi/2 and 0<r<2acos\vartheta Homework Equations I know that r=sin\varthetaThe Attempt at a Solution Im really not sure where to start my text is terrible. I really...

I have been accepted into UNC and am anticipating an acceptance letter from State. I had planned on attending State because I wasn't sure if I would get into UNC, but now that I have I can't decide where I won't to go. So my question is which school has the better math department? I plan on...

Homework Statement Determine the divergence or the convergence of the sequence. If it converges find its limit. a_{n} = (\frac{(n)!}{2n!+1}) The Attempt at a Solution All I know about factorials is for example 4! = 1*2*3*4. So as far as limits go I'm clueless. please help!

Just wanted to let everyone know that Harvard professor Shlomo Sternberg has posted some excellent material and books online. http://www.math.harvard.edu/people/SternbergShlomo.html Enjoy!

Also, when determining if an improper integral diverges. It always diverges if the limit is infinity? my text doesn't say it just gives two examples where this is the case so I wanted to check before I generalized. thanks!

I just wanted to know why the limit of arctanx as x approaches infinity is \frac{\pi}{2}. It doesn't make any sense to me.

Classical mechanics.

I substituted \frac{\sqrt{25-x^{2}}}{x} for cot So what I end up with is -\frac{\sqrt{25-x^{2}}}{25x}+c

Oh I did catch that it should be 1/25 not 25. But its still slightly off.

Well did I go wrong before I got to the sin integral? because when I checked it against the original problem it didn't match.

FYI, the original problem was \int\frac{1}{x^{2}\sqrt{25-x^{2}}}dx I used trigonometric substitution to get to the problem above.

Homework Statement 25\int\frac{1}{sin^{2}x}dxThe Attempt at a Solution I wasn't sure if I could change \frac{1}{sin^{2}x} to Csc^{2}x but when I did I ended up with -25Cotx which when I checked the integral in my calculator and it was wrong. So now I'm lost...