New posts in real-analysis

Asymptotic expansion of a series

real-analysis sequences-and-series asymptotics

How does one visualize a function with a discontinuous second derivative?

real-analysis education calculus

If $f:\mathbb{R}^n \to \mathbb{R}^n$ is continuous with convex image, and locally 1-1, must it be globally 1-1?

calculus real-analysis general-topology continuity

Every ordered field has a subfield isomorphic to $\mathbb Q$?

real-analysis field-theory ordered-fields real-numbers

A doubt in the rigorous definition of limits. [duplicate]

limits definition calculus real-analysis

An exercise from my brother: $\int_{-1}^1\frac{\ln (2x-1)}{\sqrt[\large 6]{x(1-x)(1-2x)^4}}\,dx$

calculus real-analysis integration definite-integrals improper-integrals

Theorem 6.12(a) Of Baby Rudin. Alternative Proof Of $ \int_a^b \left( f_1 + f_2 \right) d \alpha = \int_a^b f_1 d \alpha + \int_a^b f_2 d \alpha$

real-analysis integration proof-writing solution-verification alternative-proof

How can I prove the integral exists and has an upper and lower bound for the sums for a discontinuous function?

real-analysis

Show that if $\int^{\infty}_0f(x)dx$ conditionally converges then $\int^{\infty}_0f_+(x)dx$, $\int^{\infty}_0f_-(x)dx$ both diverge

real-analysis calculus

Does $\sum |\sin n| / n$ converge? [duplicate]

real-analysis sequences-and-series

Are convex functions enough to determine a measure?

real-analysis measure-theory convex-analysis

Computation of a limit involving factorial $\lim_{n \to \infty} \sqrt[n+1] {(n+1)!} - \sqrt[n] {(n)!} = \frac{1}{e}$

calculus real-analysis limits factorial radicals

Why is that the extended real line $\mathbb{\overline R}$ do not enjoy widespread use as $\mathbb{R}$?

real-analysis general-topology real-numbers

If $C$ is the Cantor set, then $C+C=[0,2]$.

real-analysis elementary-set-theory cantor-set sumset

Self study Control Theory

real-analysis general-topology differential-geometry dynamical-systems control-theory

Integral $ \int_{0}^{\infty} \ln x\left[\ln \left( \frac{x+1}{2} \right) - \frac{1}{x+1} - \psi \left( \frac{x+1}{2} \right) \right] \mathrm{d}x $

real-analysis definite-integrals improper-integrals special-functions

Double sequence, two sequences converge, but to different limits? [duplicate]

calculus real-analysis sequences-and-series convergence-divergence examples-counterexamples

What is the limit of the average value of the first $n$ terms of $(1, 2, 1, 1, 1, 2, 1, 1, 2, 1, ...)$ as $n\to\infty$?

real-analysis sequences-and-series limits

About a chain rule for Wronskians

real-analysis reference-request chain-rule wronskian

the Riemann integrability of inverse function

real-analysis