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This is also why L'Hôpital's rule is necessary for finding some limits in calculus.

(but sadly rarely usable on complex cases )

These are tricky (especially since I'm not very familiar with the hyperbolic trig functions), so I cheated and used Wolfram Alpha. http://www.wolframalpha.com/input/?i=lim_x-%3E0%281%2Fsin%28x%29%5E2-1%2Fsinh%28x%29%5E2%29If you look in the steps, it uses L'Hôpital's rule.