Monday, 9 June 2014

limits - Finding limxto0fracasinbxbsinaxx2sinax witouth L'Hopital, what is my mistake?



I was working on this question.



limx0asinbxbsinaxx2sinax



limx01x2limx01abx1abxasinbxbsinaxsinax




limx01x2limx0sinbxbxlimx0sinaxax1blimx0sinaxax



blimx01x2baa



It seems like this limit does not exist, but if you apply L'Hopital's rule you seem to get an answer. What is wrong with what I did?


Answer



One error is that
limx0sincxcx=1, not c,
so your fraction is

1x2111/b
which is still indeterminate.


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