New posts in real-analysis

$L=\lim_{x\to\infty}(f(x)+f'(x))$ exists . Which of the following statements is\are correct?

real-analysis limits

How to find: $~\min\limits_{f\in E}(\int_0^1f(x) \,dx)$

calculus real-analysis optimization contest-math

Evaluating $\sum_{k=0}^\infty \left(\frac{1}{5k+1} - \frac{1}{5k+2} - \frac{1}{5k+3} + \frac{1}{5k+4} \right)$

real-analysis sequences-and-series geometric-construction

The Cantor distribution is singular (with respect to lebesgue measure)

real-analysis measure-theory

Does the derivative of a differentiable function attain its maximum and minimum?

real-analysis calculus analysis

Proving $\int_0^\pi \frac{\log(1+x\cos (y))}{\cos y}dy=\pi \arcsin x$

calculus real-analysis integration

Evaluating a Lebesgue Integral

real-analysis integration definite-integrals lebesgue-integral

A problem from the Shortlist of the Romanian Mathematics Olympiad

real-analysis inequality definite-integrals contest-math integral-inequality

Why does the plot of $f(x)=|\cos x|-|\sin x|$ look almost piecewise linear?

real-analysis calculus algebra-precalculus trigonometry

What is the limit $\lim_{n\to\infty}\frac{1^n+2^n+3^n+\dots+n^n}{n^{n+1}}$?

real-analysis analysis limits limits-without-lhopital

An example of a bounded, continuous function on $(0,1)$ that is not uniformly continuous

real-analysis limits continuity examples-counterexamples uniform-continuity

If f is integrable, is it finite almost everywhere?

real-analysis measure-theory

Absolute convergence to a rational number

real-analysis sequences-and-series

Question regarding a proof from previous post.

real-analysis integration riemann-sum

Discrete version of dominated convergence thm

real-analysis

Integral in $n-$dimensional euclidean space

real-analysis integration analysis definite-integrals special-functions

Prove $\int_0^1\frac{\ln2-\ln\left(1+x^2\right)}{1-x}\,dx=\frac{5\pi^2}{48}-\frac{\ln^22}{4}$

real-analysis calculus integration definite-integrals improper-integrals

Does $\sum_{m=0}^{\infty} {2m\choose m} \frac{1}{4^{m}} $ converge?

real-analysis sequences-and-series divergent-series

Why is 1 raised to the power of infinity undefined? [duplicate]

calculus real-analysis analysis infinity indeterminate-forms

Derivative Bilinear map

real-analysis analysis functional-analysis banach-spaces