text: Read my other answer for the explanation for this one. :-)\n\nYou have zero on top and zero on bottom, so you can certainly go ahead and use L'hopitals.\n\nDerivative of top and bottom.\n\nCos(x) -1 becomes  (-sinx)\nand x^2 becomes 2x.\n\nNow you have -sinx / 2x which you need to evaluate for x->0. On top you have sin(0) which is zero, and on bottom 2(0) is zero. You have 0/0 again, so L'hopital again.\n\n-Sin x becomes -Cos x\n2x becomes 2.\n\nNow you get -Cosx / 2, evaluated for zero that's -1/2.\n\nHope that helped,\nUMRmathmajor