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Gwyn's user avatar
Gwyn
  • Member for 3 years, 3 months
  • Last seen more than a month ago
5 votes
3 answers
295 views

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

3 votes
1 answer
460 views

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

3 votes
1 answer
80 views

Doubts in equations involving inverse tangent and inverse sine

3 votes
2 answers
129 views

Asymptotics applied to approximate solutions of trascendental equations

2 votes
2 answers
90 views

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

2 votes
1 answer
93 views

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

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

2 votes
2 answers
495 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 $T$

2 votes
1 answer
63 views

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

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

1 vote
0 answers
57 views

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

1 vote
1 answer
85 views

Doubt about uniqueness of limit proof

1 vote
2 answers
115 views

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

1 vote
1 answer
137 views

Logic doubt about the limit definition

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 $0<x_1<2$

1 vote
2 answers
39 views

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

1 vote
1 answer
94 views

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

1 vote
2 answers
75 views

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

1 vote
2 answers
138 views

Better understanding of the meaning of implication in equations

1 vote
0 answers
31 views

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

1 vote
0 answers
70 views

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

1 vote
2 answers
70 views

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

0 votes
2 answers
103 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. $\alpha f(x)+f'(x)=0$

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 $\prod_{n=1}^{\infty} a_n^2$

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 $f^{-1}(T) \ne \varnothing$

0 votes
1 answer
77 views

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

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 $(a,+\infty)$?

0 votes
0 answers
38 views

Confusion in study of derivative of a piecewise function

0 votes
0 answers
37 views

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

0 votes
3 answers
600 views

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