Honestly, looking at the problem you gave I would initially say infinity since the sine on the bottom would go to zero as x goes to zero. I don't think that is right considering what your calculator gave. It's been too long since I've done calculus and I don't remember all the tricks anymore or I would help you out more.
*edit* Ok so I forgot, both top and bottom turn to zero. That means you should use L'Hopital's Rule. You need to take the derivative of both the top and bottom, then try the limit again.
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