User Gwyn

5 votes

3 answers

288 views

Solutions of the equation $x^x=\frac{1}{256}$

asked Jan 5, 2021 at 8:22

3 votes

1 answer

371 views

Pointwise and uniform convergence of $f_n(x)=\cos \frac{nx}{1+n^2}$

asked Jan 22, 2021 at 23:22

3 votes

1 answer

78 views

Doubts in equations involving inverse tangent and inverse sine

asked Oct 15, 2021 at 6:41

3 votes

2 answers

129 views

Asymptotics applied to approximate solutions of trascendental equations

asked Jul 23, 2022 at 7:27

2 votes

2 answers

82 views

Show that for any $x,y\in\mathbb{R}$ it is $\sqrt{1+x^2} \le \sqrt{1+y^2}+|x-y|$

asked Apr 9, 2022 at 6:43

2 votes

1 answer

80 views

Question about a proof in uniqueness of limit in Abbott's "Understanding Analysis"

asked Apr 25, 2022 at 10:45

2 votes

0 answers

39 views

Questions about my mistake in evaluating $\sum_{r=0}^{n-2} 2^r \tan \frac{\pi}{2^{n-r}}$ and its limit

asked Nov 21, 2021 at 16:13

2 votes

2 answers

453 views

Given $f$ continuous, $T>0$ and supposed $\int_x^{x+T} f(t)dt=\int_0^T f(t)dt$, show that $f$ is periodic with period $T$

asked Feb 12, 2021 at 10:35

2 votes

1 answer

62 views

Is $\frac{o(x)}{x^2}=o\left(\frac{1}{x}\right)$ for $x\to0$?

asked Dec 27, 2020 at 22:28

2 votes

1 answer

107 views

Mistake when substituting constraint $4x^2+y^2=1$ into a function $f(x,y)=x^2+y^2$ in extrema problem

asked Dec 28, 2020 at 4:55

1 vote

0 answers

53 views

Prove that if a function is bounded by $M\in\mathbb{R}$ then its limit is also bounded by $M$

asked Jan 8, 2021 at 11:59

1 vote

1 answer

79 views

Doubt about uniqueness of limit proof

asked Jan 8, 2021 at 22:26

1 vote

2 answers

113 views

Pointwise and uniform convergence of $f_n(x)=\sqrt[n]{nx^2+1}$

asked Mar 20, 2021 at 3:30

1 vote

1 answer

132 views

Logic doubt about the limit definition

asked Apr 10, 2021 at 2:30

1 vote

1 answer

56 views

Induction inequality in the study of the recursive sequence $x_{n+1}=6\frac{1+x_n}{7+x_n}$ with $0<x_1<2$

asked Jun 23, 2021 at 20:24

1 vote

2 answers

39 views

Volume of $\left \{(x,y,z) \in \mathbb{R}^3 \ s.t. \ |x| \leq y \leq 2,\sqrt{x^2+y^2} \geq 2, 0 \leq z \leq \frac{1}{\sqrt{x^2+y^2}} \right\}$

asked Jun 30, 2021 at 5:02

1 vote

1 answer

90 views

I don't agree this evaluation of the volume of $E=\{(x,y,z) \in \mathbb{R}^3 \ | \ 4 \leq x^2+y^2+z^2 \leq 9, x^2+y^2 \geq 1\}$

asked Sep 4, 2021 at 20:00

1 vote

2 answers

74 views

Show that $e^x+\sin x$ hasn't minimum in $\mathbb{R}$ only with limits and continuity

asked Sep 6, 2021 at 20:44

1 vote

2 answers

115 views

Better understanding of the meaning of implication in equations

asked Dec 4, 2020 at 9:11

1 vote

0 answers

30 views

Question about injectivity of vector valued functions knowing that one of its component is injective

asked Mar 24, 2022 at 7:33

1 vote

0 answers

70 views

Proof verification: show that $\left(\frac{n!e^n}{n^{n+1/2}}\right)_n$ is strictly decreasing

asked Feb 6, 2022 at 5:57

1 vote

2 answers

66 views

Question about a step in the proof of ratio test limit implies root test has same limit

asked Feb 16, 2022 at 10:07

0 votes

2 answers

82 views

$f$ continuous in $[a,b]$, differentiable in $(a,b)$, $f(a)=f(b)=0$, then for a real $\alpha$ there is an $x \in (a,b)$ s.t. $\alpha f(x)+f'(x)=0$

asked Mar 4, 2022 at 14:03

0 votes

0 answers

32 views

Solution verification of $\prod_{n=1}^{\infty} a_n$ and $\prod_{n=1}^{\infty} b_n$ convergent, what can be said about $\prod_{n=1}^{\infty} a_n^2$

asked Mar 11, 2022 at 6:04

0 votes

0 answers

21 views

Solution check of: $f:X \to Y$ surjective if and only if for any $T \subseteq Y,T \ne \varnothing$ it is $f^{-1}(T) \ne \varnothing$

asked Mar 22, 2022 at 1:14

0 votes

1 answer

76 views

$a_n+a_{n+1} \to \alpha$ and $a_n+a_{n+2} \to \beta$ then $\alpha=\beta$ and $a_n \to \alpha/2$

asked Jun 20, 2022 at 11:40

0 votes

1 answer

33 views

Is there a way to conclude this proof about showing the existence of $\xi>a$ such that $f'(\xi)=0$ for $f$ differentiable on $(a,+\infty)$?

asked Jul 17 at 10:10

0 votes

0 answers

36 views

Confusion in study of derivative of a piecewise function

asked Feb 24, 2021 at 7:50

0 votes

0 answers

37 views

Extrema of $f(x,y)=e^{-x^2-2y}-e^{-2x^2-y}$ in $D=\{(x,y)\in\mathbb{R}^2 \ | \ x \ge 0, y \ge 0\}$

asked Nov 28, 2021 at 11:46

0 votes

3 answers

525 views

$f(z)=\frac{1}{z}$ is not uniformly continuous in $|z|<1$, $z \ne 0$.

asked Jan 20, 2021 at 22:16

Stack Exchange Network

31 Questions

Solutions of the equation $x^x=\frac{1}{256}$

Pointwise and uniform convergence of $f_n(x)=\cos \frac{nx}{1+n^2}$

Doubts in equations involving inverse tangent and inverse sine

Asymptotics applied to approximate solutions of trascendental equations

Show that for any $x,y\in\mathbb{R}$ it is $\sqrt{1+x^2} \le \sqrt{1+y^2}+|x-y|$

Question about a proof in uniqueness of limit in Abbott's "Understanding Analysis"

Questions about my mistake in evaluating $\sum_{r=0}^{n-2} 2^r \tan \frac{\pi}{2^{n-r}}$ and its limit

Given $f$ continuous, $T>0$ and supposed $\int_x^{x+T} f(t)dt=\int_0^T f(t)dt$, show that $f$ is periodic with period $T$

Is $\frac{o(x)}{x^2}=o\left(\frac{1}{x}\right)$ for $x\to0$?

Mistake when substituting constraint $4x^2+y^2=1$ into a function $f(x,y)=x^2+y^2$ in extrema problem

Prove that if a function is bounded by $M\in\mathbb{R}$ then its limit is also bounded by $M$

Doubt about uniqueness of limit proof

Pointwise and uniform convergence of $f_n(x)=\sqrt[n]{nx^2+1}$

Logic doubt about the limit definition

Induction inequality in the study of the recursive sequence $x_{n+1}=6\frac{1+x_n}{7+x_n}$ with $0<x_1<2$

Volume of $\left \{(x,y,z) \in \mathbb{R}^3 \ s.t. \ |x| \leq y \leq 2,\sqrt{x^2+y^2} \geq 2, 0 \leq z \leq \frac{1}{\sqrt{x^2+y^2}} \right\}$

I don't agree this evaluation of the volume of $E=\{(x,y,z) \in \mathbb{R}^3 \ | \ 4 \leq x^2+y^2+z^2 \leq 9, x^2+y^2 \geq 1\}$

Show that $e^x+\sin x$ hasn't minimum in $\mathbb{R}$ only with limits and continuity

Better understanding of the meaning of implication in equations

Question about injectivity of vector valued functions knowing that one of its component is injective

Proof verification: show that $\left(\frac{n!e^n}{n^{n+1/2}}\right)_n$ is strictly decreasing

Question about a step in the proof of ratio test limit implies root test has same limit

$f$ continuous in $[a,b]$, differentiable in $(a,b)$, $f(a)=f(b)=0$, then for a real $\alpha$ there is an $x \in (a,b)$ s.t. $\alpha f(x)+f'(x)=0$

Solution verification of $\prod_{n=1}^{\infty} a_n$ and $\prod_{n=1}^{\infty} b_n$ convergent, what can be said about $\prod_{n=1}^{\infty} a_n^2$

Solution check of: $f:X \to Y$ surjective if and only if for any $T \subseteq Y,T \ne \varnothing$ it is $f^{-1}(T) \ne \varnothing$

$a_n+a_{n+1} \to \alpha$ and $a_n+a_{n+2} \to \beta$ then $\alpha=\beta$ and $a_n \to \alpha/2$

Is there a way to conclude this proof about showing the existence of $\xi>a$ such that $f'(\xi)=0$ for $f$ differentiable on $(a,+\infty)$?

Confusion in study of derivative of a piecewise function

Extrema of $f(x,y)=e^{-x^2-2y}-e^{-2x^2-y}$ in $D=\{(x,y)\in\mathbb{R}^2 \ | \ x \ge 0, y \ge 0\}$

$f(z)=\frac{1}{z}$ is not uniformly continuous in $|z|<1$, $z \ne 0$.