Newbetuts

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

Does $a_n = n\sin n$ have a convergent subsequence?

Converse of Taylor's Theorem

Change of Variable formula for a non-differentiable mapping.

Prove that $\lim_{a \to \infty} \sum_{n=1}^{\infty} \frac{(n!)^a}{n^{an}} = 1$.

If $\lim_{x \to \infty} f(x) - xf'(x)$ exists, does $\lim_{x \to\infty} f'(x)$ exist as well?

What is the sign of the integral $\int_{0}^{2\pi}e^{\sin(x)}\cos(nx)\,dx$?

Prove that $\measuredangle\gamma= 90^{\circ}$

A corollary of Arzela-Ascoli Theorem

Why isn't there a continuously differentiable surjection from $I \to I \times I$?

Epsilon delta for proving $x^2$ is continuous for $x<0$

nondecreasing rearrangement is equimeasurable

Number of Fixed Point(s) of a Differentiable Function

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$

Show that $\int_0^{\infty}\frac{f(ax)-f(bx)}{x}dx=[f(0)-L]\ln\frac{b}{a}$ [duplicate]

Proving that $\sup_{s \in [a,b)}f(s)=\sup_{s \in [a,b)\cap \mathbb{Q}}f(s)$ for right continuous function.

New posts in real-analysis

More general Frullani's [closed]

Lindelöf and second countable spaces

Does $\infty$ mean $+\infty$ in "English mathematics"?

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

Does $a_n = n\sin n$ have a convergent subsequence?

Converse of Taylor's Theorem

Change of Variable formula for a non-differentiable mapping.

Prove that $\lim_{a \to \infty} \sum_{n=1}^{\infty} \frac{(n!)^a}{n^{an}} = 1$.

If $\lim_{x \to \infty} f(x) - xf'(x)$ exists, does $\lim_{x \to\infty} f'(x)$ exist as well?

What is the sign of the integral $\int_{0}^{2\pi}e^{\sin(x)}\cos(nx)\,dx$?

Prove that $\measuredangle\gamma= 90^{\circ}$

A corollary of Arzela-Ascoli Theorem

Why isn't there a continuously differentiable surjection from $I \to I \times I$?

Epsilon delta for proving $x^2$ is continuous for $x<0$

nondecreasing rearrangement is equimeasurable

Number of Fixed Point(s) of a Differentiable Function

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$

Show that $\int_0^{\infty}\frac{f(ax)-f(bx)}{x}dx=[f(0)-L]\ln\frac{b}{a}$ [duplicate]

Proving that $\sup_{s \in [a,b)}f(s)=\sup_{s \in [a,b)\cap \mathbb{Q}}f(s)$ for right continuous function.