Recent content by ypatia

Is there any function (if any) f: Z -> Z such that f(f(n))=-n , for every n belongs to Z(integers) ?? I think that there is not any function like the one described above but how can we prove it. Any ideas?? Thanks in Advance

No I don't

Homework Statement How can we found the length of the curve: f(x) = \frac {1}{12}(x - 48)\sqrt x where x\ge0 and the vertical line x=48. Homework Equations The Attempt at a Solution I tried to use the formula L=\int^{48}_{0}\sqrt {1 + \ [f'(x)]^2} dx But I think that...

What do you mean as a first step?? Then I will calculate the two integrals. Is it Ok?? Thanks xepma!

Homework Statement I'm a little a bit confused about the following exercise because of the two segments of the function. How can we find the Laplace transform of this function f(t) = \begin {cases} t , 0\le t < 4 \\ 5 , t\ge 4\end {cases} Homework Equations The Attempt at a...

Ptolemy metric space. Help! The problem is : "Let x,y,z,t belongs to R^n where d(x,y)=||x-y||. Show that(Ptolemy's inequality): d(x,y)d(z,t)<=d(x,z)d(y,t)+d(x,t)d(y,z)" I have found this related to the topic paper but I cannot show that the Euclidean space R^n is Ptolemy. The paper...