
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 3rd, 2017, 04:43 AM  #1 
Member Joined: Jan 2015 From: usa Posts: 75 Thanks: 0  Inequality with $sinh$ and $cosh$
We consider a parameter $a>>1$ and we note $cosh(\theta)=\sqrt{4a+1}$ and $sinh(\theta)=2\sqrt{a}$ for all $t>0$ we note: $u(t)=\frac{\sinh(\frac{t}{2}\cosh(\theta))}{\cosh (\theta)}$ $A(t)=\frac{\sqrt{\cosh^2(\theta)u^2(t)+1}1}{\cosh^2(\theta)}\Big(\cosh(\frac{t}{2})1\Big)$ $f(t)=ln\Big(1\frac{2A(t)}{u(t)+\sinh(t)+A(t)}\Big)$ I want to find the minimal power $\alpha\ge 0$ such that $$\frac{\cosh^2(\theta)}{f(t)}e^{argsh(u(t))}\le \frac{\theta^{\alpha}}{t^3}$$ for all $t>0$ 
November 3rd, 2017, 07:24 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,659 Thanks: 652 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
November 3rd, 2017, 09:12 AM  #3 
Member Joined: Jan 2015 From: usa Posts: 75 Thanks: 0 
$\theta$ is fixed from the begining

November 4th, 2017, 07:32 AM  #4 
Member Joined: Jan 2015 From: usa Posts: 75 Thanks: 0 
@topsquark, can you help me to prove the iniquality by taking $\alpha=4$? 

Tags 
$cosh$, $sinh$, inequality 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to solve cosh(y)sin(x) = 1 and sinh(y)cos(x) = 1  Lalaluye  Complex Analysis  2  January 27th, 2017 05:53 PM 
Solving three cosh(x) equations with three variables  iman.sayah  Applied Math  5  January 10th, 2014 09:29 PM 
Geometric interpretation of sinh,cosh  Singularity  Complex Analysis  3  December 9th, 2010 06:23 AM 
derivative of cosh(Ax) =?  boardsportsrule  Calculus  2  March 14th, 2009 08:19 PM 
Verify add. formula for cosh  jens  Calculus  3  October 22nd, 2008 02:52 AM 