exercise with arctg and (probably) differntial

Kangurur

New member
Joined
Nov 18, 2020
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1
\(\displaystyle xarctgx>(1/2) (pi)-1\)


\(\displaystyle x>=0\)
I have no idea how to solve this. Help me please🥺
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
6,874
This does NOT involve a differential and certainly is NOT a differential equation! There is no "formula" or "trick" to this, just look for values of x so that \(\displaystyle x arctan(x)= 0\). It is simply algebra- solve this equation.

I would start by using "Desmos", https://www.desmos.com/calculator, to graph \(\displaystyle y= x arctan(x)\) and \(\displaystyle y= \frac{\pi}{2}- 1\). It appears that \(\displaystyle x arctan(x)>\frac{\pi}{2}\) for x< -0.826 and x> 0.826, approximately.
 
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