#math - Sun 22 Apr 2007 between 19:36 and 19:49

NY Lost Funds



linoliumis the negative zero of 2^x = x^2 irrational?
zaphyBeeblex=2
Manyfoldi always thought 0 has no sign
powerfox|Steve|: Thanks!
|Steve|np
linoliummaybe I'm using the wrong term here.. but I get x = 2, 4, and -0.766665
zaphyBeebleyep x=4
|Steve|There appear to be 2 negative solutions that mathematica can find.
They are definitely not rational.
linoliumtwo?!
zaphyBeeblehow does it solve it?
|Steve|But they might be the same. I can't tell.
Oh, one of them turned out to be 4.
zaphyBeeblex log 2 = 2 log x => log 2 /2 = log x / x
|Steve|(-2*ProductLog[-1, -Log[2]/2])/Log[2] is what it found
% Simplify[ (-2*ProductLog[-1, -Log[2]/2])/Log[2]]
mbot|Steve|: (-2*ProductLog[-1, -Log[2]/2])/Log[2]
|Steve|% FullSimplify[ (-2*ProductLog[-1, -Log[2]/2])/Log[2]]
mbot|Steve|: 4
linoliumwhat does ProductLog do?
|Steve|No idea.
Olathe% ProductLog::usage
mbotOlathe: "ProductLog[z] gives the principal solution for w in z = w e^w. ProductLog[k, z] gives the kth solution."
akSeyahi there...
how to solve this inequation: ((x+1)/(2-x))<(x/(3+x))
powerfox|Steve|: I don't know what to do next :(
|Steve|powerfox: Partial fraction decomposition.
RadSurferIf I wanted to find a pdf theory on how triple integrals work, and what they are applied too, could someone help me?
randomityakSeya: multiply both sides by (2-x)^2*(3+x)^2 ?
|Steve|pdf being probability density function?
powerfox|Steve|: ok, thanks. I will try
OlatheakSeya: Multiply both sides by 2-x. You should get two answers: one if 2-x is positive, one if it's negative.
akSeyarandomity, i tried to multiply (x+1)(3+x)<x(2-x)
randomity, can you tell me why i cant do that way?
zaphyBeeblei think randomity's was better..always +ve
OlatheakSeya: If you multiply both sides by a negative, it changes the direction of the inequality.
zaphyBeebleand u get a cubic olathe if u do it randomity's way..hrmf...
OlatheRight.
|Steve|Is it so hard to figure out when (2-x)(x+3) is negative though?
zaphyBeebleso does it mean one more possibilty of x ?

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