Question Number 50398 by Abdo msup. last updated on 16/Dec/18
$${find}\:{lim}_{{t}\rightarrow+\infty} \:\:\:\frac{{sh}\left(\sqrt{{t}^{\mathrm{2}} +{t}}\right)−{sh}\sqrt{{t}^{\mathrm{2}} −{t}}}{\left(\mathrm{1}+\frac{\mathrm{1}}{{t}}\right)^{{t}^{\mathrm{2}} } \:\:−\frac{{t}^{\mathrm{6}} }{\mathrm{6}}{ln}^{\mathrm{2}} \left({t}\right)} \\ $$