December 9th, 2017, 07:56 AM  #1 
Senior Member Joined: Jan 2015 From: usa Posts: 101 Thanks: 0  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 08:33 AM. 

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