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Sep
24
awarded  Popular Question
Sep
24
awarded  Popular Question
Jul
2
awarded  Yearling
May
13
awarded  Caucus
Apr
9
comment Infinite sets don't exist!?
You could mention, that Von Neumann proposed that all natural numbers can be bootstrapped out of the empty set by the operation you described.
Mar
28
awarded  Popular Question
Mar
28
awarded  Popular Question
Mar
4
awarded  Popular Question
Feb
18
answered $E^2[X]$ vs.$E[X^2]$, what's the difference?
Jan
27
awarded  Tumbleweed
Jan
20
asked Properties of shortest walks and simple paths during optimization
Jan
20
accepted Parameterized curve describing trajectory of thrown object
Jan
16
comment When is $f(x) = \frac{ax}{e^{-b}-{(e^{c})}^x}$ monotonic?
By the way, is this a homework related question? If so, then please consider adding the appropriate tag - furthermore show what you have done so far and what you don't understand so we see that you at least tried something.
Jan
16
answered When is $f(x) = \frac{ax}{e^{-b}-{(e^{c})}^x}$ monotonic?
Jan
14
comment Parameterized curve describing trajectory of thrown object
I don't know whether this is correct, but we never did such complicated computations in class. I tried to solve this problem now by not factorizing so that I have $\sqrt{v_0^2\cos^2\beta+(v_0\sin\beta-gt)^2}$ and simplify that with other (much easier) approaches. Do you have some other suggestions?
Jan
14
comment Parameterized curve describing trajectory of thrown object
Actually I never saw this method, but I think that this yields $\int \|k'(u)\|\,\mathrm du=\frac{1}{2}g\left(u-\frac{v_0\sin(\beta)}{g}\right)^2+v_0\cos(\beta)u+\text{c‌​onstant}$. Did I understand this substitution right?
Jan
14
asked Parameterized curve describing trajectory of thrown object
Jan
8
comment Proving that $\left(\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\cdots+\frac{1}{n!}\right)$ has a limit
Careful, you say that $x_n$ is a finite sum and saying that it equals an infinite sum. Furthermore you ambiguously use $n$. These are just small mistakes with the notation. How about saying $\lim_{n\to \infty} x_n = \lim_{n\to \infty} \frac{1}{0!}+\ldots+\frac{1}{n!}=\sum_{k=0}^{\infty}\frac{1}{k!}=e$?
Jan
7
comment If $\sum_{n=1}^\infty a_n$ is convergent, then $\sum_{n=1}^{\infty} a_n\sin(n)$
@GEdgar: I thought about that fact that $|\sin(n)|\leq 1$ like Andrew mentioned this could be an "easier" example to simplify $\sin$ if you understand.
Jan
7
revised If $\sum_{n=1}^\infty a_n$ is convergent, then $\sum_{n=1}^{\infty} a_n\sin(n)$
edited body