Hi guys, i'm trying to figure out if this is true or not, can you help me?
Conjecture: Let f:[m,+∞)->R be a continuous and monotonous function with a horizontal asymptote y0 (as x->+∞). Then:
1) f is derivable.
2) f'->0 as x->∞.
I ask for f being monotonous because the only counterexamples, to the non-improved conjecture, that came to my mind are things like f(x)=sin(x^2)/x.
Thanks in advance.
I'm studying some demonstrations about 2nd order differential equations of the form:
where a,b are constants.
Suppose that u,v are linearly independent solutions. Now, in several demonstrations, it's needed that the Wronksian determinant of u,v it's different from zero.
I see from Abel's identity (http://en.wikipedia.org/wiki/Abel's_identity) that if this is true for some t0 value, then it's true for all t. Provided this, can I always say that the Wronksian of u,v is always non-zero??
Hi there! These are very simple and smart proofs. I suggest you also to give a look to:
Book1, Prop.48, Prop.49
the second one (if i remember good) is the Inverse theorem (i.e. if a triangle is such that c²=a²+b², then it's rectangle).
if I may, it seems to me that the (logical) error is deeper:
is just a symbol to denote the class of antiderivatives; so, saying class=number makes me think 21122012 is totally missing the meaning of it all.
Here a problem here in what:
Calculus doesn't distinguish an arithmetic increment from a geometrical increment! ! !
Calculus - bad science! ! !
I'm sorry, but I really don't find the connection you see beetwen this and the main topic...
However, don't you feel a little ashamed by saying "Calculus - bad science! ! !"??
I may be wrong, because i read your first post and didn't either understand what you're talking about... but, honestly, seems to me (and not only to me, as I see) you don't know what an indefinite integral is.
To be brief, the "tauists", as they call themselves, argue that the constant pi should be replaced with tau=2*pi, which is much more natural.
I have to say that, to me, the manifesto was really convincing; as i see it, the use of tau instead of pi brings clarity and coherence with other formulas (for example area of a circular sector).
What do you think about it?
I may be wrong, but I think stating that:
is an error, is itself a (logical) error. Because the indefinite integral is DEFINED AS the solution to the problem:
It is the antiderivative, and what you gave is just the definition... does it make any sense to ask if is a definition right or wrong?
Saying that ∫f(x)dx=F(x)+C is an error seems to me like saying that it's wrong to put the ' to indicate the derivative...
I could have totally missed the point, maybe for example your paper says the defining the indefinite integral this way leads to some contradiction; in case i hope you can explain us.
How does this look? :0)
i*180 i*(180/n) i0
(-1)^(1/n) = (1*e )^(1/n) = 1*e so this approaches 1*e = 1 as n goes to infinity.
(The angles are in degrees.)
I have to admit that at first sight this looked funny; but after being (maybe) less superficial i'm seeing a meaning behind this:
look it geometrically (i write polar coordinates for complex numbers)...
the (first) square root for -1 is (1,pi/2) (midnight)
the (first) 3rd root for -1 (1,pi/3) (one o'clock)
the (first) 4th root for -1 is (1,pi/4) (half past one)
..... (...some time passes...)
the (first) nth root for -1 tends to (1,0) (almost three o' clock)
so it seems to me that your limit is what the first nth root of (-1) tends to.
EDIT: I want to add something:where k=0,1,2...,n-1. In particular, the integer part of (n+1)/2 (which is n/2 if n is even and (n+1)/2 if odd) belongs to the list of k's;
(where i put n/2 or n+1/2 as k)
so one of us (or eventually both ) must be wrong.
hi mitu, I would say it does not exist if your succession is from N to R;
here's a short proof of non-existence:
if LIM[a(n)]=L, then for all a(n(k)) LIM[a(n(k))]=L
you see that LIM[a(2k)]!=L since a(2k) is not defined for each k. But maybe someone would argue that for each n in dom(a(n)) a(n)=-1, so LIMa(n)=-1... i see it just as a formal problem, maybe someone can be more precise.
While writing my post i realized that if your succession is from N to C it is not even a function, so i don't know if it has any meaning to talk about limit...
It is just a conjecture that i've made so i'm asking if you can prove it or give a counterexample.
My conjecture :
let A(n) be the square matrix (n+1)x(n+1) with the generic element be
[Link fixed by admin]
I've tested it to n=9...
moreover, det(A) seems to diverge to +inf with n and i've not found a negative value.
hope someone finds this interesting, goodbye!