F feyomi Jan 2010 50 0 May 26, 2010 #1 Let a > 0. Let x ϵ (0,a) and y ϵ (0,a). Use the fact that cosh is a primitive of sinh to prove that |sinh y - sinh x| ≤ (cosh a)|y - x| Thanks very much for any help. Last edited: May 26, 2010

Let a > 0. Let x ϵ (0,a) and y ϵ (0,a). Use the fact that cosh is a primitive of sinh to prove that |sinh y - sinh x| ≤ (cosh a)|y - x| Thanks very much for any help.

P Plato MHF Helper Aug 2006 22,458 8,632 May 26, 2010 #2 Use the mean value on \(\displaystyle \sinh(t)\) on the interval \(\displaystyle [x,y]\). Note that \(\displaystyle \cosh(c)\le \cosh(a)\) if \(\displaystyle c<a\). Reactions: HallsofIvy and feyomi

Use the mean value on \(\displaystyle \sinh(t)\) on the interval \(\displaystyle [x,y]\). Note that \(\displaystyle \cosh(c)\le \cosh(a)\) if \(\displaystyle c<a\).