New posts in real-analysis

Schwartz Class Functions on Integers

Approximate Holder continuous functions by smooth functions

real-analysis partial-differential-equations approximation holder-spaces

How much larger is the $\sigma$-algebra than the algebra in Caratheodory extension?

real-analysis probability analysis measure-theory reference-request

Divergence of a vector field on a sequence of spheres

calculus real-analysis integration sequences-and-series

Derivative of Linear Map

calculus real-analysis linear-algebra general-topology

Proof that if $f$ is integrable then also $f^2$ is integrable

real-analysis integration

Existence of a Strictly Increasing, Continuous Function whose Derivative is 0 a.e. on $\mathbb{R}$

real-analysis measure-theory

Calculating 2 integrals in polylogarithmic functions

calculus real-analysis integration definite-integrals

are singletons always closed?

real-analysis general-topology metric-spaces

Proving continuity and monotonicity of $t\mapsto t^x, t>0$ with minimal assumptions.

Prove that $f(ax + (1-a)y) = \frac{1}{y-x}\int_x^y f(t)dt$ implies $a = \frac{1}{2}$

real-analysis integration definite-integrals

Show that Hill's Equation $u'' + a(t)u=0$ if $a(t)<0$ for all $t$ then $u\to\infty$ as $t\to\infty$

real-analysis ordinary-differential-equations

prove this inequality with $63$

real-analysis multivariable-calculus inequality uvw mixing-variables

Counterexample to Riemann sum limit

real-analysis examples-counterexamples riemann-integration

How can I study the convergence of the improper integral $\int_{0}^{ \infty} \frac{\sin(x)}{x+1} \, \mathrm dx\,$?

real-analysis integration convergence-divergence improper-integrals

How to prove that $S=\sum_{n=0}^{\infty}\frac{(\sqrt{2}-1)^{2n+1}}{(2n+1)^2}=\frac{\pi^2}{16}-\frac{1}{4}\log^2(\sqrt{2}-1)?$

real-analysis calculus integration sequences-and-series

How do I evaluate $\int_{-1}^1\frac{dx}{(1+x^2)(e^x+1)}$?

real-analysis calculus integration

$\{(x,f(x)): x\in E\}$ is compact in $\mathbb R^2 \implies f:E\to\mathbb R$ is continuous

real-analysis analysis solution-verification proof-explanation

Functions from the Cantor set

real-analysis continuity cantor-set

Does there exist a sequence of real numbers $\{a_n\}$ such that $\sum_na_n^k$ converges for $k=1$ but diverges for every other odd positive integer?

real-analysis sequences-and-series analysis convergence-divergence contest-math