Math Forum / Mathematics / General Topics / April 2007

Writing a paper about Taylor Series, but I don't understand how I
find
the error or where the formula for the error comes from..
can anyone

I don't know where did the post go when I tried to post it before so here is
again.
Hello. I'm preparing for the test tomorrow and I got stuck on this problem.
When coin 1 is flipped, it lands heads with probability .4; when coin 2 is

Let X1, X2,....Xn be exchangeable random variables
with E|Xi|<infty
and Let Sn=X1+ X2+ .... +Xn.
What is E(X1 | Sn)?

Hello. I was solving a problem but I got a different answer than my friend.
Could anyone tell me which answer is wrong and where is a mistake?
The problem is:
Three balls are to be randomly selected with replacement from an urn

I am trying to prove a theorem about the relationship between the
vertex colouring number (chromatic number) of a graph and the minimum
number of edges in that graph.  My book states that: if the chromatic
number of a graph is n, the number of edges in that graph must be at

suppose A is a m X n matrix that maps any x in R^n to y in R^m. If
this mapping is to be one to one, does it require det(A) to be
nonzero?
thanks

Looking at the mod 18 table and then
making a comparison with the differences
between the pures I cam up with this
table.

I would like to hear your comments on my proof (i hope) of the Riemann
Hypothesis (RH)
http://www.dse.nl/%7Egeertjan/Publikatie/Proof_of_the_Riemann_Hypothesis_v2.pdf
And if you are an endorser on arXiv, and you find the proof valid, please

I'm preparing for my final and have the following question--this is not graded hw nor a test question.
Prove or disprove: If G=F union H then x(G) <= x(F) + x(H) where x(K) means the chromatic number of K. It seem that the statement is true but I can't write up a proof.
Thanks

can a non planar graph have a chromatic coloring of 2?
Thanks.

My book says the MVT does not generalize to vector valued functions,
but the following version does:
a*[f(y) - f(x)] = a*[ f'(z)(y-x)]
where * means dot product and f'(z) is the total derivative of f at

Can anyone help me out here please:
The equations ux = v^2 + y and vy = x^2 + 2u^2 define u and v as
functions of the independent variables x and y. Show that:
(du/dx) = (uy-4xv) / (8uv-xy)

On a maths exam, I will be required to  "Computing the Hessians of
exotic functions". I never heard about the concept "exotic function".
I just guess it is not a quadratic function but I am not sure.  Would
anyone out there tell me what it is?

Any ideas about evaluate symbolically the following integral?
Integrate[1/Sqrt[(1 - x^2)*(4 - x^2)*(9 - x^2)*(16 - x^2)],{x,0,1}]
Thanks!
Dimitris

by the way, so far I've derived the theorem and formula and
investigated certain functions with the Approximation. But I need to
write 2 more pages, one with the Error and one with the Local Extremes.