Newbetuts

Finding the closed form of $\int_0^1 \frac{(1-x+x\log x)\operatorname{Li}_3(x)}{x(x-1) \log x} \ dx$

Let $f$ be a continuous and differentiable function such that $f(a)=f(b)=0$ , show that $f'(c)=\pi f(c)$ for some $c \in (a,b)$

Series with $\zeta$

limit $ \lim \limits_{n \to \infty} {\left(\frac{z^{1/\sqrt n} + z^{-1/\sqrt n}}{2}\right)^n} $

limsup of the product of two sequences, of which one converges

Does, $\lim\limits_{x \to +\infty } f'(x) = + \infty \Leftrightarrow \lim\limits_{x \to +\infty } \frac{{f(x)}}{x} = + \infty $?

If a set is open, does it mean that every point is an interior point? [duplicate]

Binomial analogue of Riemann sum for definite integral

negation of mathematical statements- Real Analysis example

Why is $(10/x)^x$ biggest when $10/x = e$?

Determine the rate of convergence

$f$ don't have local minimum or local maximum in $c$

Green’s Function for the Heat Equation

Let $C \subseteq [0,1]$ be uncountable, show there exists $a \in (0,1)$ such that $C \cap [a,1] $ is uncountable

Prove that if $S$ is a finite set then $S$ has no limit points.

Calculating Dini derivatives for $f(x)=\begin{cases}x\,\sin{\left(\frac{1}{x}\right)} & x\neq 0\\ 0 & x=0\end{cases}$

$\Delta x$ in limit problem?

New posts in real-analysis

Integrability of Derivative of a Continuous Function

Continuous function and Hausdorff space

A question about a mathematical analysis book

Finding the closed form of $\int_0^1 \frac{(1-x+x\log x)\operatorname{Li}_3(x)}{x(x-1) \log x} \ dx$

Let $f$ be a continuous and differentiable function such that $f(a)=f(b)=0$ , show that $f'(c)=\pi f(c)$ for some $c \in (a,b)$

Series with $\zeta$

limit $ \lim \limits_{n \to \infty} {\left(\frac{z^{1/\sqrt n} + z^{-1/\sqrt n}}{2}\right)^n} $

limsup of the product of two sequences, of which one converges

Does, $\lim\limits_{x \to +\infty } f'(x) = + \infty \Leftrightarrow \lim\limits_{x \to +\infty } \frac{{f(x)}}{x} = + \infty $?

If a set is open, does it mean that every point is an interior point? [duplicate]

Binomial analogue of Riemann sum for definite integral

negation of mathematical statements- Real Analysis example

Why is $(10/x)^x$ biggest when $10/x = e$?

Determine the rate of convergence

$f$ don't have local minimum or local maximum in $c$

Green’s Function for the Heat Equation

Let $C \subseteq [0,1]$ be uncountable, show there exists $a \in (0,1)$ such that $C \cap [a,1] $ is uncountable

Prove that if $S$ is a finite set then $S$ has no limit points.

Calculating Dini derivatives for $f(x)=\begin{cases}x\,\sin{\left(\frac{1}{x}\right)} & x\neq 0\\ 0 & x=0\end{cases}$

$\Delta x$ in limit problem?