2
$\begingroup$

I want to prove the inequality $3x\cdot \mathrm{arccot}{x}\geq\ln(1+x^{2})$... using Cauchy's theorem..I saw this in a book which I bought in a library and ive never seen this type of exercise..can you solve it ?

  • 3
    You can find some good starting points on how to format mathematics on the site [here](http://meta.math.stackexchange.com/a/464/264) and [here](http://meta.stackexchange.com/a/70559/161783). [This AMS reference](ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf) is very useful. If you need to format more advanced things, there are many excellent references on LaTeX on the internet, including StackExchange's own [TeX.SE](http://tex.stackexchange.com/) site.2012-12-26

2 Answers 2

1

You may need to modify the function, or the interval. Compute $3x\,\text{arccot}\,x-\ln(1+x^2)$ at $x=10$. The result is negative.

0

It's true for $0 \le x \le 4.246876095$ approximately, not true outside that interval. What interval did you want to prove it on?