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1d
revised Problems understanding definition of limit superior.
Some backslashes
1d
comment Problems understanding definition of limit superior.
As $k$ gets larger, the union gets smaller (it contains fewer numbers), so the supremum may decrease.
Jul
24
comment How to calculate intermediate points in spline?
You can look at it this way: Your curve would have the form $p(t)=q((t-a)/(b-a))$ (for $t\in[a,b]$) where $q$ is a standard Bézier curve on $[0,1]$. Thus $p'(t)=q'((t-a)/(b-a))/(b-a)$, in particular $p'(a)=q'(0)/(b-a)$. You want to plug in $q'(0)$ in place of $v_1$ in the formula, but $q'(0)=(b-a)p'(a)$, so the control points would be $p(a)$, $p(a)+\frac13(b-a)p'(a)$, $p(b)-\frac13(b-a)p'(b)$, and $p(b)$. (And if I managed to get it backwards – which I don't think I did – you should divide by $(b-a)$ instead.)
Jul
24
comment Why, or why not, is $5^{log_3(n)} \in \mathcal{O}(n^2)$?
Yep. Better write that with curly brackets, though: $n^{\log_3}(5)$ to get $n^{\log_3}(5)$. (Oh, I see you found that out while I was writing this.) Note the backslash on the log. Also don't use the asterisk $*$ for multiplication outside of programming. In mathematics, it has a different meaning (usually convolution). I edited the question for you.
Jul
24
revised Why, or why not, is $5^{log_3(n)} \in \mathcal{O}(n^2)$?
Backslash on logs, and don't use * for multiplication
Jul
24
comment Why, or why not, is $5^{log_3(n)} \in \mathcal{O}(n^2)$?
Another quick tip: $a^{bc}=(a^b)^c$.
Jul
22
comment Does an isotropic vector always exist for an indefinite quadratic forms?
Yeah, that's right.
Jul
22
comment Does an isotropic vector always exist for an indefinite quadratic forms?
No, but its restriction to any finite dimensional subspace is continuous, and that is all we need here.
Jul
22
answered Does an isotropic vector always exist for an indefinite quadratic forms?
Jul
22
comment How to prove this limit in $\ell_1$
TeX allows you to write \limsup for limit superior. Also, \| for the norm. I fixed them for you. But anyhow, I fail to detect a question. Do you ask if the stated equality holds, or are you asking for help to prove it? What did you try? A free hint: To prove equalities involving inf, sup, liminf or limsup, try to prove that each side is $\le$ the other.
Jul
22
revised How to prove this limit in $\ell_1$
Fixed LaTeX formatting
Jul
22
comment A problem on nested radicals
The fourth power of $x=\sqrt{a-b\sqrt{a+bx}}$ (which I think you should have) would be $x^4=a^2-2ab\sqrt{a+bx}+b^2(a+bx)$.
Jul
22
comment A problem on nested radicals
No, before that. (I edited my comment while you were answering it.)
Jul
22
comment A problem on nested radicals
Can you explain the simplification you did when taking the fourth power? It does not look right. Oh, wait a minute: Same thing with the initial equation for $x$. Or did you mean to ask about $x=\sqrt{(a-b)\sqrt{(a+b)\sqrt{(a-b){\sqrt{(a+b)\sqrt{…}}}}}}$ ?
Jul
22
answered How to calculate intermediate points in spline?
Jul
17
comment Not a basis for $ l^\infty$ then what is it?
@martini I know – I was already looking for a way to insert a star when your answer popped up and showed me one way to do it. … Now fixed (and I got rid of the extra space too).
Jul
17
answered Not a basis for $ l^\infty$ then what is it?
Jul
13
comment $\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$
You could try to rewrite the sum to look like a Riemann sum.
Jul
11
comment Looking for a hint on the following integration problem
The point of my hints are these, in plain language rather than in mathematese: The function $nx^n$ has total “weight” very close to 1 as $n$ grows big, and almost all of that “weight” is concentrated near $x=1$. So your integral is computing a weighted average of $f$, with almost all of the weight concentrated around $x=1$. Of course that is going to get you $f(1)$, almost – meaning exactly, in the limit. The answer by @OliverOloa is a good way to translate that insight into a rigorous proof.
Jul
11
answered Looking for a hint on the following integration problem