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1d
answered Proving existence of Itō Integral
May
25
comment Integration by parts prove integral of cos^n x dx
To get started, write $\cos^n x$ as $\cos^{n-1}x\cdot\cos x$ and do some partial integration.
May
15
comment Show that $\sin(\mathcal{o}(x)) = \mathcal{o}(x)$ as $ x\to 0$
The mean value theorem works fine. In fact, the inequality $|\sin x|\le|x|$ is an immediate consequence of the mean value theorem applied to $\sin 0$ and $\sin x$.
May
15
comment Show that $\sin(\mathcal{o}(x)) = \mathcal{o}(x)$ as $ x\to 0$
You could use the relation $\cos(2x)=1-2\sin^2(x)$. And lo, you get $\cos(o(x))=1+o(x^2)$, which is even better.
May
15
answered Show that $\sin(\mathcal{o}(x)) = \mathcal{o}(x)$ as $ x\to 0$
May
11
answered Limit of square root where x approaches infinity
May
10
answered A linear map to a finite-dimensional space is injective iff it's a section
May
7
revised Bound for derivative of analytic function on a disk
Fix too quick 'n dirty calculation
May
7
comment Bound for derivative of analytic function on a disk
@BloodBorne You're right, that does not make sense. However, the calculation can be saved by doing the integral more carefully – it can in fact be calculated exactly. I'll edit the answer accordingly.
Apr
27
comment Norms that $C([0,1])$ to be an incomplete normed space.
@epimorphic You're right, I was a bit hasty there. However, the claim is true for bounded sequences (bounded in the usual uniform norm, that is). And that is sufficient for the present purpose of making a divergent Cauchy sequence. Thanks for point out the mistake. (I am not going to edit the answer. Let future readers look at the comments.)
Apr
21
comment 1 to the power of infinity, why is it indeterminate?
@Noein: Oops, thanks for pointing it out. In order to not gratuitously bump this to the front page, I will let it stand as is. Hopefully, people will read the comments if the mistake confuses them.
Apr
11
comment Angle Sum of Self-intersecting polygon
@JayLemmon I don't think I claimed that the summing to $\pm2\pi$ is sufficient for the polygon to be non-self-intersecting. It will be sufficient if all the turns have the same sign; then the polygon will be convex. But in general, counterexamples are quite easy to make, as you say.
Mar
29
comment How to prove that Pumping lemma can't be used to prove regular languages.
It seems you need an example of a non-regular language which satisfies the conclusion of the pumping lemma. Does that help?
Mar
23
comment Convergence of sequence of a function
You might try playing with the function $f(x)=\sin(1/x)$ for $x\ne0$, $f(0)=0$, and $c=0$.
Mar
21
answered logarithmic limit in R^n
Mar
10
awarded  Informed
Mar
9
comment Let $p_n$ be the $n$th prime, for any integer $n$, prove that: $p_n+p_{n+1}\geq{p_{n+2}}$
@DDaren \sim will come out as $\sim$.
Mar
9
comment Can $n^4 + n^3 + n^2 + n + 1$ for $n \in \mathbb{N} \backslash \{ 0,3\}$ yield a perfect square number?
@Silenttiffy Because we're looking for a perfect square, meaning the square of an integer, so $n^2+n/2+x$ has to be an integer. Given that $n$ is an integer, that means $2x$ must be an integer.
Mar
7
comment Can $n^4 + n^3 + n^2 + n + 1$ for $n \in \mathbb{N} \backslash \{ 0,3\}$ yield a perfect square number?
@Silenttiffy Try $x=0$: $(n^2+n/2)^2=n^4+n^3+n^2/4<n^4+n^3+n^2+n+1$. Or try $x=1$: $(n^2+n/2+1)^2=n^4+n^3+\frac94n^2+n+1>n^4+n^3+n^2+n+1$.
Mar
5
answered Deduce that if $A$ is a subset of $C$, then $\sup A\leq \sup C$.