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Daniil
  • Member for 2 years, 11 months
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6 votes
1 answer
168 views

Show that the sequence defined as $x_{n+1}=\frac{1}{1+x_n}$ converge

6 votes
3 answers
599 views

Uniformly continuous function on bounded open interval is bounded

5 votes
1 answer
103 views

$f:\mathbb{R} \mapsto \mathbb{R}$ convex and increasing. Show there is $a \in \mathbb{R}$ such that $\lim\limits_{x\to -\infty}\frac{f(x)}{x}=a$

5 votes
1 answer
111 views

Intuition on product definition in category theory

5 votes
1 answer
95 views

$|f(x)-f(y)|\leq \|x-y\|^2$ implies $f$ is constant

4 votes
2 answers
55 views

Let $g\in G$ such that $o(g)=n<\infty$ (of a finite order). Show that $o(g^r)=\frac{n}{(n,r)}, 0<r<n$

4 votes
3 answers
246 views

Show that the sequence defined as $x_{n+1}=\sqrt[3]{x_n+x_{n-1}}$ converges

4 votes
2 answers
114 views

$g(x) = \frac{f'(x)}{f(x)}$ not bounded

3 votes
1 answer
206 views

$(f_n)$ sequence of differentiable functions on $[0,1]$ and converge pointwise to $0$.

3 votes
0 answers
99 views

Show that the sequence defined as $x_{n+1}=\frac{1}{2}(x_n+x_{n-1})$ is convergent [duplicate]

3 votes
1 answer
246 views

Show that $f$ is Riemann-Integrable

3 votes
1 answer
303 views

Show that $f$ is Riemann Integrable on $\left[0,\pi/2\right]$

3 votes
0 answers
125 views

Let $f(x)=\frac{1}{n}$ if $x=\frac{1}{n}$ and $f(x)=0$ if not. Show that $f$ is Riemann integrable

2 votes
1 answer
126 views

Show that $f(x)=x$ if $x\in\mathbf{Q}$ and $f(x)=1-x$ if $x \in\mathbf{R}/\mathbf{Q}$ is Riemann integrable on $[0,1]$

2 votes
1 answer
67 views

Let $f\in C([a,b])$ and $\int_{a}^{x}f=\int_{x}^{b}f \ \forall x\in[a,b]$. Show that $f=0$ on $[a,b]$.

2 votes
1 answer
119 views

Let $f\in C([a,b])$, $\int_{a}^{b}f(x)\phi'(x) \ dx=0$ for all continuous and differentiable functions $\phi$. Show $f$ is constant

2 votes
2 answers
102 views

Let $f$ differentiable on $(a, \infty)$ such that $\lim_{x\to\infty}\frac{f(x)}{x}=0$. Show that $\lim\inf_{x\to\infty}|f'(x)|=0$

2 votes
1 answer
137 views

Let $f_n$ sequence of continuous functions on $[a,b]$, $\lim_{n\to \infty}f_n(x)=f(x)$ uniformly on $(a,b)$. Show $f_n\mapsto f$ uniformly on $[a,b]$

2 votes
2 answers
80 views

Convergence of $\sum_{n=0}^{\infty}a_n/n$ if $\sum_{n=0}^{\infty}a_n^2$ exists [duplicate]

2 votes
1 answer
81 views

Absolute convergence of $\sum_{n=0}^{\infty}a_nb_n$ if $\sum_{n=0}^{\infty}b_n^2$ and $\sum_{n=0}^{\infty}a_n^2$ converge

2 votes
1 answer
57 views

Prove that the sequence defined as $x_{n+1}=\frac{2x_n+5}{6}, x_0=\frac{1}{2}$ converges

2 votes
2 answers
77 views

Show that $\lim_{n \to \infty}(b_1b_2...b_n)^{\frac{1}{n}}=b$

2 votes
1 answer
75 views

Convergence of $\sum_{n=0}^{\infty}a_nb_n$ if $a_n>0 \ \forall n\in \mathbf{N}$, $\sum_{n=0}^{\infty}a_n$ converges and $b_n$ bounded

2 votes
0 answers
87 views

Show that $f$ on $[0,1]$ is Riemann integrable [duplicate]

2 votes
3 answers
55 views

Show that the sequence $x_{n+1}=5x_n-4x_{n-1}$ diverge

2 votes
1 answer
236 views

Construction of Steiner Porism with concentric circles

2 votes
1 answer
262 views

How can we construct radical axis of 2 circles where one is inside the other one?

2 votes
1 answer
181 views

Find non trivial homomorphism $\mathbb{Z}/q\mathbb{Z} \rightarrow \text{Aut}(\mathbb{Z}/p\mathbb{Z})$

2 votes
5 answers
299 views

Is every subgroup of $S_n$ cyclic?

2 votes
1 answer
47 views

For $n,i>0$ find a normalizer of $\langle \tau \sigma^i\rangle$ in $D_{2n }$