Tuesday, 5 August 2014

Calculate the limit limxto0fracarcsin(2x)ln(e2x)1 without using L'Hôpital's rule




I need to calculate the limit without using L'Hôpital's rule:



limx0arcsin(2x)ln(e2x)1



I know that: lima0arcsinaa=1



But, how to apply this formula?


Answer



We have, limx0arcsin2xln(e2x)1=limx0arcsin2x2x2xln(e2x)1=limx0arcsin2x2x2xeln(1+(2xe))×(e)

This can be easily simplified to get the answer as e. Hope it helps.


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