New posts in real-analysis

Is it always true that $\mathrm{int}(\ A \setminus \mathrm{int}(A)\ ) = \emptyset$?

real-analysis general-topology

liminf and limsup with characteristic (indicator) function

real-analysis elementary-set-theory limsup-and-liminf

Terms that get closer and closer together [duplicate]

real-analysis sequences-and-series convergence-divergence

Proof $\lim_{x \rightarrow \infty}f(x)=\lim_{x \rightarrow 0^{+}}f(\frac{1}{x})$

real-analysis calculus

Proving the divergence of a infinite integral

real-analysis integration improper-integrals

Evaluate: $\lim_{n\to\infty} \int_a^{\infty}\frac{n^2xe^{-n^2x^2}}{1+x^2}\,dx.$

real-analysis measure-theory lebesgue-integral

Uniform convergence of $\sum (-1)^nf_n(x)$ on $[0,1]$ where $f_n(x)=x^n(1-x)$.

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

Exchange of two limits of a function

Distance function is in fact a metric

real-analysis metric-spaces

Discontinuity of Thomae Function on $\mathbb{Q}$

real-analysis continuity

Prove for bounded $f$, if $f:[a,r] \to \mathbb{R}$ is Riemann-Integrable for $r \in [a,b)$ then $f:[a.b] \to \mathbb{R}$ is Riemann-Integrable

real-analysis riemann-integration

Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$

real-analysis compactness

Applying MVT and IVT (?) to show something about f'''? (edit: actually, Taylor's Theorem using Lagrange remainder)

calculus real-analysis derivatives taylor-expansion

Need help with a proof that if $xy=0$ then $x=0$ or $y=0$

Nowhere continuous function limit

real-analysis limits epsilon-delta

How to evaluate $\lim_{x\to 0} \frac{x^2\sin {\frac{1}{x}}}{\sin x}$

real-analysis limits trigonometry

Find $a$ and $b$ for which $\int_{0}^{1}( ax+b+\frac{1}{1+x^{2}} )^{2}\,dx$ takes its minimum possible value.

real-analysis calculus integration multivariable-calculus optimization

Motivation for Topology study in Real Analysis

real-analysis general-topology soft-question

bounded variation functions on $[0,1]$ are always $L_2[0,1]$?

real-analysis functional-analysis lp-spaces bounded-variation

A question 2019 Putnam A6