I think that my previous reply has been deleted, or I never was able to post it and thought I did.
By the way, I actually did not conceive the number
0.9999999999...
aritmetically.
I mean... what are these dots?
The only way I saw this was through a limit of a serie.
With this point of...
That's very easy to show, once you can use the theorem "f continuous on a compact => f uniformly continuous", even though I had to stress some tecnichal detail.
Take eps > 0.
You have to find a delta > 0 such that for every couple of elements x1, x2 in [0, +infty) such that | x1 - x2 | <...
The proof I wrote actually shows it DOES NOT converge.
I can't proof it diverges to +infinity yet.
My proof is very tecnical and LONG and actually there are some points a bit difficoult that I have to clear out before to call an EXACT proof.
I need help!
You are right! sqrt(2) does not exist.
And in fact also 1 does not exist.
1 is the multiplication of 13/7 and 7/13 now
13/7 and 7/13 are just symbols for their decimal representations which are
13/7 = 1,85714285...
7/13 = 0,53846153...
and the decimal places continue on infinitely.
So...
Since
2sin(x)cos(x) = sin(2x)
you can write the integrand function
x/2 \cdot \sin (2x)
you can use first the substitution
y=2x
and then use integration by part formula to integrate
y/4 \cdot \sin (y)
it is EASY if you choose to derive y/4 and integrate \sin(y).
This is not an homework, but just a couriosity that I have
I never found a easy way to solve the question of convergence of this serie
\sum_n (\sin(n))^n
any help is appreciated!
well, in my modest opinion, since
1 = (-1)(-1) = (-1)(-1)1 = (-1)(-1)(-1)(-1) = ... = ((-1)^(2n))(1^m)
for every n,m natural,
you should put your question under some rule of irredundance to try to find a interesting answer.
The (powerful) Vitali theorem states that a bounded function f: D \subset \mathbb R \longrightarrow \mathbb R defined on a bounded domain is Riemann integrable IF AND ONLY IF it has a set of point of discontinuity of measure zero.
Now in your function you have that [a,b] is the set of the...
well, there is uniform convergence of the succession of functions of circles to the function
constant = 0 in the interval (say) [0,1] now the elements of the succession have a graph that has constant length \pi, but the limit has a graph of length 1.
Well that's not a paradox, also more...
A classroom has 2 rows of 8 seats. There are 14 students, 5 of whom always sit in the front row and 4 whom always sit in the back.
In the first row there are always 5 students that will seat.
In how many ways they can sit?
It is the number of injective functions from a set of 5 elements in a...
To place the two red you have to select a subset of two elements in a set of 36.
So you have a number of choices equal to the combinations of 36 on 2 that is
36*35/2 = 18*35 choices.
Then you have to place the four blue and you have a number of choices equal to the
number of the subsets of...
You are WELCOME!
Well I also noticed I made a 'print' mistake...
in the last row
I wrote [F:E] instead of
[F: F \cap E]
but I guess you noticed the mistake and you got the right meaning.
See you next time!