New posts in real-analysis

Continuous functions that pointwise converge to zero, but the integral tending towards infinity.

If $f'$ is bounded, then $f$ is uniformly continuous

real-analysis uniform-continuity

Evaluating $\lim_{n\rightarrow\infty} \int_{0}^{\pi} \frac {\sin x}{1+ \cos^2 (nx)} dx$

real-analysis integration limits proof-verification definite-integrals

The $n$-th derivative of $x^2(x+1)^n$?

real-analysis derivatives

Average Frequency of 1's in an Infinite Binary Sequences Can be Anything Between 0 and 1

real-analysis probability sequences-and-series probability-theory

The sum of infinitely many $c$s is $c$ implies $c = 0$.

real-analysis algebra-precalculus probability-theory measure-theory

Prove that: $\int_{0}^{1} \frac{x^{4}\log x}{x^2-1}\le \frac{1}{8}$

real-analysis integration inequality

If $\{f_n\}$ is a measurable sequence of functions, then $\{x : \lim f_n(x) $ exists $\}$ is measurable

real-analysis measure-theory

Integral of an increasing function is convex?

real-analysis integration convex-analysis

Constructing a set with exactly three limit points

Proving that there is an irrational number between any two unequal rational numbers.

Prove that the set of integer coefficients polynomials is countable

real-analysis elementary-set-theory polynomials

Show that: $\inf(A+B) = \inf(A)+ \inf(B)$

real-analysis solution-verification supremum-and-infimum

$f$ is integrable, prove $F(x) = \int_{-\infty}^x f(t) dt$ is uniformly continuous.

Deriving Taylor series without applying Taylor's theorem.

calculus real-analysis taylor-expansion recreational-mathematics

a sequence $\{s_n\}$ with $\sum s_n$ convergent

real-analysis sequences-and-series

Issue with Spivak's Solution

calculus real-analysis analysis continuity

If $f(x)$ is smooth and odd, must $f(x)/x$ be smooth?

real-analysis smooth-functions

What is value of this integral? $\int_{0}^{\infty}\frac{\log(1+4x^2)(1+9x^2)(9+x^2)+(9+x^2)\log(4+x^2)(10+10x^2)}{(9+x^2)^{2}(1+9x^{2})}dx$

real-analysis calculus integration sequences-and-series improper-integrals

Regarding integrals of type $f(x)=\int_{a}^{b}g{(x+f(x))}dx$

real-analysis calculus integration definite-integrals