Newbetuts

How to estimate $ \left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$?

Prove inequalty

A function that satisfies the Intermediate Value Theorem and takes each value only finitely many times is continuous.

Integral equation

Prove/Show that Limit is equal to 0.

Asymptotic estimation of $A_n$

How do I prove that the second derivative of a function $f:M\to\mathbb{R}$ defined on a surface $M\subset\mathbb{R}^n$ is well defined?

Let $S=\{p(x) \in \mathbb Z[X] :|p(x)| \leq 2^x, \forall x\in \mathbb N\}$. Prove $|S| < \infty$

Does there exist a bijection $f$ from $\mathbb{N}$ to $\mathbb{Q}^+$ such that $\lim_{n \to \infty} \frac{f(n+1)}{f(n)}$ exists?

Splitting a continuous monotonically-increasing function $f(x)$ as $h(x)+h(x+\epsilon) = f(x)$

Computing a limit of a sum mixed with product.

Image of closed ball under degenerate integral operator is a closed set

Apply implicit function theorem on $z^3 - 3xyz = 1$ and $z = z(x,y)$

Summation of divergent series of Euler: $0!-1!+2!-3!+\cdots$

Why are monotone functions Riemann integrable on a closed interval?

How many continuous function $f(x)$ exist such that $\int_{0}^{1}f(x)\big(1-f(x)\big)\mathrm dx = \frac{1}{4}$? [closed]

Counterexample of multiplicative Landau inequality in finite interval

New posts in real-analysis

difficult problem in riemman integrals

Total variation measure vs. total variation function

A Vitali set is non-measurable, direct proof, without using countable additivity

How to estimate $ \left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$?

Prove inequalty

A function that satisfies the Intermediate Value Theorem and takes each value only finitely many times is continuous.

Integral equation

Prove/Show that Limit is equal to 0.

Asymptotic estimation of $A_n$

How do I prove that the second derivative of a function $f:M\to\mathbb{R}$ defined on a surface $M\subset\mathbb{R}^n$ is well defined?

Let $S=\{p(x) \in \mathbb Z[X] :|p(x)| \leq 2^x, \forall x\in \mathbb N\}$. Prove $|S| < \infty$

Does there exist a bijection $f$ from $\mathbb{N}$ to $\mathbb{Q}^+$ such that $\lim_{n \to \infty} \frac{f(n+1)}{f(n)}$ exists?

Splitting a continuous monotonically-increasing function $f(x)$ as $h(x)+h(x+\epsilon) = f(x)$

Computing a limit of a sum mixed with product.

Image of closed ball under degenerate integral operator is a closed set

Apply implicit function theorem on $z^3 - 3xyz = 1$ and $z = z(x,y)$

Summation of divergent series of Euler: $0!-1!+2!-3!+\cdots$

Why are monotone functions Riemann integrable on a closed interval?

How many continuous function $f(x)$ exist such that $\int_{0}^{1}f(x)\big(1-f(x)\big)\mathrm dx = \frac{1}{4}$? [closed]

Counterexample of multiplicative Landau inequality in finite interval