New posts in real-analysis

Properties of real analytic function [duplicate]

real-analysis taylor-expansion analytic-functions

Prove that if $f$ is bounded and nondecreasing on $(a,b)$ then lim $f(x) $as $x$ approaches $b$ from the left exists.

How to prove $E\subset R^n$ Jordan measurable is equivalent to $\bar{E}-E$ is Jordan measured null

real-analysis measure-theory

dense in $\mathbb{R}$ and dense in $[0,1]$ modulus $1$

Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$ [duplicate]

calculus real-analysis limits

Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence? [duplicate]

real-analysis calculus analysis convergence-divergence divergent-series

Behaviour of the sequence $u_n = \frac{\sqrt{n}}{4^n}\binom{2n}{n}$

calculus real-analysis sequences-and-series math-software

Book Recommendations and Proofs for a First Course in Real Analysis

real-analysis reference-request soft-question book-recommendation

Is the set of discontinuity of $f$ countable?

If series $\sum a_n$ is convergent with positive terms does $\sum \sin a_n$ also converge?

calculus real-analysis sequences-and-series limits

Let $f :\mathbb{R}→ \mathbb{R}$ be a function such that $f^2$ and $f^3$ are differentiable. Is $f$ differentiable?

real-analysis complex-analysis functions derivatives

What determines if a function has a least positive period?

real-analysis periodic-functions

Let $f: \mathbb{R} \to \mathbb{R}$ be continuous periodic function with period $T>0$

real-analysis continuity periodic-functions

Volume of $n$ dimensional ellipsoid

real-analysis linear-algebra integration measure-theory

$f(x,y) = \frac{x^3y}{x^4 + y^2}$ is not differentiable at $(0,0)$.

real-analysis derivatives frechet-derivative

Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.

real-analysis metric-spaces

Continuity of the function $f(x,y)=\frac{\cos(x+y)+\cos(x-y) -2}{x^2 +y^2 }$

real-analysis multivariable-calculus continuity

Hilbert cube is compact

real-analysis hilbert-spaces compactness lp-spaces

Prove that $\int_0^\infty \frac{e^{\cos(ax)}\cos\left(\sin (ax)+bx\right)}{c^2+x^2}dx =\frac{\pi}{2c}\exp\left(e^{-ac}-bc\right)$

calculus real-analysis integration definite-integrals improper-integrals

Rudin's proof that the Cantor set has no segments

real-analysis cantor-set