\displaystyle\lim_{x\to +\infty}(ch(\frac{1}{\sqrt x}))^x=[1^+^\infty]=e^{\displaystyle\lim_{x\to +\infty}(ch(\frac{1}{\sqrt x})-1)*x}=e^{\displaystyle\lim_{x\to +\infty}\frac{ch(\frac{1}{\sqrt x})-1}{(\frac{1}{\sqrt x})^2}}=e^\frac{1}{2}=\sqrt e