Newbetuts

When do we have $\liminf_{n\to\infty}(a_n+b_n)=\liminf_{n\to\infty}(a_n)+\liminf_{n\to\infty}(b_n)$?

Evaluating $\int_0^\infty \left| \frac{\sin t}{t} \right|^n \, \mathrm{d}t$ for $n = 3, 5, 7, \dots$

Can a function have a positive derivative at a point but not be increasing/decreasing around that point?

$\sigma$-finite measure and semi-finite measure

If $f$ has an invertible derivative at some point $x$, then $f$ is 1-1 on some neighborhood of $x$.

Proving that if $a^2+b^2=c^2$, then $a+b\ge c$.

Limit of Lebesgue integral $\int_F \; \frac{dx}{2 - \sin nx}$

Mean value property with fixed radius

Can we make $\mathbb{R}^{2}$ an ordered field?

Proving that product of two Cauchy sequences is Cauchy

Convergence power series in boundary

limit of absolute value of something equals absolute value of limit of something?

Fourier transform of a real function is real

Existence of a map $f: \mathbb{Z}\rightarrow \mathbb{Q}$

Radon Nikodym Thm: extending to $\sigma$-finite case

Epsilon - delta proof $\lim_{x \to \frac{\pi}{4}} \tan(x)=1$

pointwise convergence but not L1 convergence

Compute $\lim_{n\to\infty}n^4\int_0^1\frac{x^n\ln^3x}{1+x^n}\ln(1-x)\,dx$

New posts in real-analysis

When do we have $\liminf_{n\to\infty}(a_n+b_n)=\liminf_{n\to\infty}(a_n)+\liminf_{n\to\infty}(b_n)$?

Two inequalities about using Fatou Lemma

Finding $f$ such that $f(f(f(f...(x)))) = x$

Evaluating $\int_0^\infty \left| \frac{\sin t}{t} \right|^n \, \mathrm{d}t$ for $n = 3, 5, 7, \dots$

Can a function have a positive derivative at a point but not be increasing/decreasing around that point?

$\sigma$-finite measure and semi-finite measure

If $f$ has an invertible derivative at some point $x$, then $f$ is 1-1 on some neighborhood of $x$.

Proving that if $a^2+b^2=c^2$, then $a+b\ge c$.

Limit of Lebesgue integral $\int_F \; \frac{dx}{2 - \sin nx}$

Mean value property with fixed radius

Can we make $\mathbb{R}^{2}$ an ordered field?

Proving that product of two Cauchy sequences is Cauchy

Convergence power series in boundary

limit of absolute value of something equals absolute value of limit of something?

Fourier transform of a real function is real

Existence of a map $f: \mathbb{Z}\rightarrow \mathbb{Q}$

Radon Nikodym Thm: extending to $\sigma$-finite case

Epsilon - delta proof $\lim_{x \to \frac{\pi}{4}} \tan(x)=1$

pointwise convergence but not L1 convergence

Compute $\lim_{n\to\infty}n^4\int_0^1\frac{x^n\ln^3x}{1+x^n}\ln(1-x)\,dx$