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  • 366 votes cast
Dec
22
accepted Diagonalizable transmit to submatrix
Dec
18
asked Diagonalizable transmit to submatrix
Dec
8
asked Estimate $\sum_{\left|\frac{k}{n}-x\right|>\delta}\binom nk x^k(1-x)^{n-k}$
Dec
3
accepted If a separately continuous function $f : [0,1]^2 \to \mathbb{R}$ vanishes on a dense set, must it vanish on the whole set?
Dec
1
asked If a separately continuous function $f : [0,1]^2 \to \mathbb{R}$ vanishes on a dense set, must it vanish on the whole set?
Nov
26
accepted Find $\lim (a_{n+1}^\alpha-a_n^\alpha)$
Nov
21
revised The continuous relationship between $f(x,y)$ and $\varphi(x)=\lim f(x,y)$
edited tags
Nov
21
asked The continuous relationship between $f(x,y)$ and $\varphi(x)=\lim f(x,y)$
Nov
20
comment Show $\sum_{n=1}^\infty \frac 1n\,\sin\left(\Bigl(n-\frac 12\Bigr)\pi+\frac xn\right)$ converges uniformly and continuously differentiable.
I think $\sum f_n$ converges uniformly is not use M test. When $n > a$, then $\cos(x/n)/n $ is $\rightarrow 0$ monotonously. Then use Leibniz Test.
Nov
20
comment Show that the derivative of a function is not continuous
$g'(x)=\begin{cases} 1+4x\sin\frac{1}{x}-2\cos\frac{1}{x}&\text{ if }x\neq0\\\ 1&\text{ if }x=0 \end{cases}$ $g'(\frac{1}{2n\pi})<0$, $g'(\frac{1}{2n\pi+\pi/2})>0$,By intermediate value theorem $\exists \frac{1}{2n\pi+\pi/2}<x_n<\frac{1}{2n\pi}$, $g'(x_n)=0$. I don't know how to construct the concrete $x_n$
Nov
19
asked An sufficient condition for $\lim_{x\rightarrow x_0}\lim_{y\rightarrow y_0}f(x,y)=\lim_{y\rightarrow y_0}\lim_{x\rightarrow x_0}f(x,y)$
Nov
15
accepted Show there exists $\xi \in [a,b]$ such that $g(\xi)\int_a^\xi f(x)\text{d}x=f(\xi)\int_\xi^b g(x)\text{d}x$
Nov
15
asked Show there exists $\xi \in [a,b]$ such that $g(\xi)\int_a^\xi f(x)\text{d}x=f(\xi)\int_\xi^b g(x)\text{d}x$
Nov
5
asked Find $\lim (a_{n+1}^\alpha-a_n^\alpha)$
Nov
1
awarded  Nice Question
Oct
24
awarded  Popular Question
Oct
12
awarded  Yearling
Sep
21
asked $\mathcal{F}=\{S\subset E: \exists A\in \mathcal{B}(S\supset A)\}$ + $\mathcal{F}$ is a filter $\Rightarrow$ $\mathcal{B}$ is a filter base.
Sep
20
accepted How many ways to show $\sum_{n=1}^{\infty}\ln \left|1-\frac{x^2}{n^2\pi^2}\right|$ is pointwise convergence?
Sep
19
revised How many ways to show $\sum_{n=1}^{\infty}\ln \left|1-\frac{x^2}{n^2\pi^2}\right|$ is pointwise convergence?
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