prove or disprove: $\lim_{x\to \infty} \frac{f(x)}{g(x)}=\lim \frac{f'(x)}{g'(x)}=0 \implies \lim \frac{\frac{f(x)}{g(x)}}{\frac{f'(x)}{g'(x)}}\ne 0$

Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$

Number of all labeled, unordered rooted trees with $n$ vertices and $k$ leaves.

Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$

Solving $\phi(n)=84$

Big-O and function composition

What cubic problems did Tartaglia and Fior pose to each other?

Are there 3 trig functions or are there 6 trig functions?

Why do we call primes, and not the number one, *the atoms of numbers*?

Why is $\mathbb{R}/\mathbb{Z}$ isomorphic to the complex numbers of module one?

Simplify the expression $(2n)!/(2n+2)!$

Problem 6 - IMO 1985

Prove that $\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}}+\frac{1}{\sqrt{1+c^2}}\le\frac{3}{2}$

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