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Apr
14
accepted Find minimum of $a+b$ under the condition $\frac{m^2}{a^2}+\frac{n^2}{b^2}=1$ where $m,n$ are fixed arguments
Apr
14
asked Find minimum of $a+b$ under the condition $\frac{m^2}{a^2}+\frac{n^2}{b^2}=1$ where $m,n$ are fixed arguments
Apr
3
asked Estimate the bound of the sum of the roots of $1/x+\ln x=a$ where $a>1$
Apr
3
awarded  Notable Question
Feb
12
accepted $1+xy+yz+xz-x-y-z>0$ where $x,y,z \in (0,1)$
Feb
11
asked $1+xy+yz+xz-x-y-z>0$ where $x,y,z \in (0,1)$
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 $\lim (a_{n+1}^\alpha-a_n^\alpha)$