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 Real Analysis Real Analysis Math Forum

 November 6th, 2017, 01:06 AM #1 Senior Member   Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 Simplification of a formula We consider a fixed parameter $\theta>0$. For all $t>0$ we note: $$u(t)=\frac{\sinh\big(\frac{t}{2}\cosh(\theta)\bi g)}{\cosh(\theta)}$$ $$A(t)=\frac{\sqrt{\cosh^2(\theta)u^2(t)+1}-1}{\cosh^2(\theta)}-\Big(\cosh\Big(\frac{t}{2}\Big)-1\Big)$$ $$f(t)=-\ln\Big(1-\frac{2A(t)}{u(t)+\sinh(t)+A(t)}\Big)$$ For all $\theta>0$ the equation 2\sinh\Big(cosh(\theta)t\Big)\sinh\Big(t\Big)=1 where $t>0$ has a unique solution that we note $t^*>0$. I want to know if we can simplify $f(t^*)$ or either find a constant $c>0$ such that $f(t^*)\ge c$?? Please help me . Thanks. Tags formula, simplification Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ku5htr1m Calculus 6 October 12th, 2016 04:36 PM 3uler Trigonometry 1 February 3rd, 2015 03:08 AM p3aul Algebra 5 January 23rd, 2011 09:11 PM wulfgarpro Algebra 7 April 18th, 2010 03:16 AM arron1990 Calculus 1 December 31st, 1969 04:00 PM

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