Convergence of $\frac{\sinh^2(x)}{\sinh^2(x) + C}$ as $x \to \infty$ I was wondering if someone could help me conclude what happens when I set $x\rightarrow\infty$ for the following equation where $C\in\mathbb{R}$:
$$\lim_{x\rightarrow\infty}\frac{\sinh^2(x)}{\sinh^2(x) + C}$$
I just do not know where to go with this. It is related to a physics problem I am doing.

Observe that
$$\frac{\sinh^2(x)}{\sinh^2(x)+C}=\frac{\sinh^2(x)+C-C}{\sinh^2(x)+C}\\=1-\frac C{\sinh^2(x)+C}$$
And then the limit is hopefully more clear.
