TITLE: Prove that $\lim\limits_{x \to 0} \sinh(x)/x =1$.
QUESTION [9 upvotes]: Prove that $ \lim\limits_{x \to 0} \frac{\sinh x}{x} =1.$

I am having some trouble proving this without derivative. Some help would be much appreciate!

REPLY [3 votes]: You could use the squeeze theorem with bounding functions 1 and $e^{|x|}$