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 December 9th, 2017, 07:56 AM #1 Senior Member   Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 Inequality Let $\nu>1$ be a parameter. For all $t>0,\;\;\;$ we consider $A(t)=\frac{1-cos(t\sqrt{4\nu-1})}{4\nu-1}-(\cosh(t)-1)$ $g(t)=\frac{2A(t)}{\frac{sin(t\sqrt{4\nu-1})}{\sqrt{4\nu-1}}+\sinh(t)+A(t)}$ $f(t)=\frac{\sqrt{\nu }\;t^{\frac{3}{2}}\;e^{-t\nu^\frac{1}{3}}}{ln(1-g(t))}$ >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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