New posts in real-analysis

Divergence of $\sum\limits_n1/\max(a_n,b_n)$

real-analysis sequences-and-series

Change of Summation and Differentiation

calculus real-analysis

Show the series $ \sum_{j=1}^{\infty} \frac{(2^j)+ j}{(3^j) - j} $ converges

real-analysis sequences-and-series

Sequence of simple functions nonnegative that converge to measurable function $f$

real-analysis measure-theory

How do I evaluate the Lebesgue measure of a ball?

real-analysis measure-theory

$f$ is continuous $ \iff $ $f^{-1}$ is continuous?

real-analysis continuity inverse

$f(x)=x^2$ is not Lipschitz?

calculus real-analysis uniform-continuity lipschitz-functions

If $ \int_0^{\pi}f(x)\cos(nx)\,dx=0$ for all $n$ then prove that $f\equiv 0$

real-analysis integration analysis definite-integrals

(Somewhat) generalised mean value theorem

real-analysis integration derivatives

Compute the integral $\int_{-1}^1 \frac{|x-y|^{\alpha}}{(1 - x^2)^{\frac{1+\alpha}{2}}}dx = \frac{\pi}{\cos(\pi \alpha/2)}$

real-analysis integration definite-integrals

root of an odd degree polynomial

If $f$ continuous and $\lim_{x\to-\infty }f(x)=\lim_{x\to\infty }f(x)=+\infty $ then $f$ takes its minimum.

real-analysis proof-verification

Limit of $h_n(x)=x^{1+\frac{1}{2n-1}}$

How do I use the Intermediate Value Theorem in this question?

real-analysis continuity

Is every norm increasing?

real-analysis normed-spaces

Does parity matter for $\lim_{n\to \infty}\left(\ln 2 -\left(-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots -\frac{(-1)^n}{n}\right)\right)^n =\sqrt{e}$?

real-analysis integration sequences-and-series limits summation

Prove $ \int_{5\pi/36}^{7\pi/36} \ln (\cot t )dt +\int_{\pi/36}^{3\pi/36} \ln (\cot t )dt = \frac49G $

real-analysis calculus integration definite-integrals catalans-constant

Differentiable at a point

calculus real-analysis soft-question definition

Confusion in GH Hardy's proof of $\lim_{x\to \infty} (f(x)+f'(x))=0\implies \lim_{x\to \infty} f(x)=0 \land \lim_{x\to \infty} f'(x)=0$

real-analysis proof-explanation

If a function $ f $ is continuously differentiable and $ \int_0^{\infty} f(x)dx$ converges then $ f $ is bounded.

real-analysis improper-integrals riemann-integration