Friday, 28 November 2014

limits - Avoid L'hopital's rule




limx0ln(cosx)sin2x=?



I can solve this by using L'Hopital's rule but how would I do this without this?


Answer



log(cos(x))sin2(x)=12log(1sin2(x))sin2(x)=sin2(x)+O(sin4(x))2sin2(x)x012.


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