New posts in real-analysis

Prove that $\int_{0}^{1} \frac{\ln(x)}{x-1} dx = \sum_{k=1}^{\infty} \frac{1}{k^2}$

real-analysis calculus sequences-and-series solution-verification uniform-convergence

How to calculate this improper integral?

real-analysis calculus analysis improper-integrals

$\bigg(\int_{0}^{\infty}(\int_{0}^{x}|f(t)|dt)^{p}x^{-b-1}dx\bigg)^{1/p}\le p/b\bigg(\int_{0}^{\infty}|f(t)|^{p}t^{p-b-1}dt\bigg)^{1/p}$

real-analysis lp-spaces

A proof of Taylor's Peano Remainder using little o notation

real-analysis calculus number-theory numerical-methods asymptotics

A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$

calculus real-analysis sequences-and-series limits convergence-divergence

Folland's Real Analysis 7.11

real-analysis measure-theory

Series in Real Analysis

If $x_n\leq y_n$ then $\lim x_n\leq \lim y_n$ [duplicate]

real-analysis sequences-and-series limits inequality

Show $\max{\{a,b\}}=\frac1{2}(a+b+|a-b|)$

real-analysis algebra-precalculus proof-verification absolute-value

Example of a countable compact set in the real numbers [closed]

real-analysis metric-spaces

Product of measurable functions is measurable

Evaluate $\int_{0}^{\infty} \frac{{(1+x)}^{-n}}{\log^2 x+\pi^2} \ dx, \space n\ge1$

calculus real-analysis integration improper-integrals

Pointwise limit of integrable function

Calculate the limit $\lim \limits_{n \to \infty} |\sin(\pi \sqrt{n^2+n+1})|$

real-analysis limits trigonometry radicals

Suppose $(a_n)$ is a sequence such that $a_n=\frac{1!+2!+\cdots+n!}{n!}$. Show that $\lim{a_n}=1$

If $\lim_{x\to\infty}\frac{f'(x)}{f(x)}=1$, is $f$ asymptotic to $\exp$?

real-analysis calculus limits asymptotics exponential-function

$f \in \mathcal{R}[a, b]$, $g$ is a bounded real-valued function on $[a, b]$ s.t. $f(x) = g(x)$ almost everywhere. Is $g \in \mathcal{R}[a, b]$?

Nowhere continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f\bigl(f(x)\bigr) = \frac{f(2x)}{2}$ [closed]

real-analysis calculus functions continuity functional-equations

Analytic expression for the primitive of square root of a quadratic

calculus real-analysis integration

If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$ [duplicate]

real-analysis limits