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If $$f(x) = \dfrac{{\displaystyle 3\int_{0}^{x}(1 + \sec t)\log\sec t\,dt}}{(\log\sec x)\{x + \log(\sec x + \tan x)\}}$$ then prove that $...

An (approximate) non-negative rational number representation is a pair of natural numbers each not greater than some fixed limit M (and of c...

I was reading the book Seventeen equations have changed the world . At some point, while the book was talking about complex numbers, I see t...

$$ x=1+\cfrac{1}{1+\cfrac{1}{1+...}}\implies x=1+\frac{1}{x}\implies x=\frac{1\pm \sqrt{5}}{2} $$ Can the negative solution be considered as...

relations between the root test and the ratio test I know the theorem is correct if they are exist $$ \lim\inf\limits_{n\rightarrow \infty} ...

So this multi-valued function $f(z) = \sqrt{r}e^{i \frac{\theta}{2}}$ is multi-valued because it can output multiple results with a single ...

Suppose we have non-negative measurable functions $f_n$ which are square integrable on a finite measure space $\Omega$, i.e. $\mu(\Omega) $$...