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Originally Posted by Amadeus  ^ Thank you so much, Jhevon! It really helped me a lot. 
But I'd like to check to see if my answers are right. 
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CaptainBlack already told you this was correct
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remember, we were multiplying by an x here, and the x went to zero, so the second limit went to 1 and we multiplied by zero
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3.  <-- I think that one is wrong...
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here, you seem to have caught the fact that the x made us multiply by zero, however, the x was a typo (sorry) it should have been cos(x). (you should have caught that though, and i also mentioned that the limit simplified to sin(x)/x, so that's a second thing you should have caught)
you should get
(h is going to zero, there should be no h in your final answer, did you try my suggestion?)