New posts in Analysis

Does there exist a bijection that is not eventually equal to the identity, but has a finite number of "crosses"?

To show a sequence is bounded, monotone and to find its limit

Can we define a derivative on the $p$-adic numbers?

Simple proof that the Airy function decays faster than any polynomial

Given positive real numbers $a$, $b$, $c$, $d$, $e$ with $\sum_{\text{cyc}}\,\frac{1}{4+a}=1$, prove that $\sum_{\text{cyc}}\,\frac{a}{4+a^2}\le1$.

Evaluating the $ \lim_{n \to \infty} \prod_{1\leq k \leq n} (1+\frac{k}{n})^{1/k}$

limit of the sequence $x_{n}:= \sqrt[n]{n \sqrt[n]{n \sqrt[n]{n\ldots}}}$

Prove or Disprove : There exists a continuous bijection from $\mathbb{ R}^2$ to $\mathbb{R} $

Existence of $A$ such that $ \lim_{x\to\infty}\operatorname{poly}(x) e^{-x} \sum_{n\in A} \frac{x^n}{n!}=1 $

Prove that the integral $\int_a^b \frac{\sin(x)}{x}dx$ is bounded uniformly.