December 9th, 2017, 08:56 AM  #1 
Senior Member Joined: Jan 2015 From: usa Posts: 103 Thanks: 1  Inequality
Let $\nu>1$ be a parameter. For all $t>0,\;\;\;$ we consider $A(t)=\frac{1cos(t\sqrt{4\nu1})}{4\nu1}(\cosh(t)1)$ $g(t)=\frac{2A(t)}{\frac{sin(t\sqrt{4\nu1})}{\sqrt{4\nu1}}+\sinh(t)+A(t)}$ $f(t)=\frac{\sqrt{\nu }\;t^{\frac{3}{2}}\;e^{t\nu^\frac{1}{3}}}{ln(1g(t))}$ >I want to prove that there exists a constant $c>0$ which dosn't depend on the parameter $\nu$ such that: $$f(t)\le c$$ for all $t>0$ Please help me to do so. Thanks. Last edited by mona123; December 9th, 2017 at 09:33 AM. 

Tags 
inequality 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Triangle Inequality: Prove Absolute Value Inequality  StillAlive  Calculus  5  September 3rd, 2016 12:45 AM 
An inequality  Dacu  Algebra  10  April 6th, 2014 07:27 PM 
Inequality  Ionika  Algebra  0  February 17th, 2014 03:29 AM 
inequality  JC  Algebra  6  October 29th, 2011 05:32 PM 
Inequality  Gustav  Algebra  11  February 28th, 2011 07:04 AM 