Wednesday, May 11, 2016

limits - Solving limxto0xlnx



I needed to solve



limx0xlnx



and I wasn't sure how I would do it so I looked up the answer.



They used L'Hoptial to solve this and I don't understand why this works.




limx0xlnx=limx0lnx1/x but I can't use L'Hopital here because this is



undefined0, so I looked up if ln 0 is really undefined and it turns out that the limit of ln0 is infinity



My textbook says I can only use L'Hopital with infinf or 00, so why am I allowed to use L'Hopital in this case?


Answer



You can use L'Hopital if you rewrite your expression lnx1/x



As x0+, we have the indeterminate form of , so you are now licensed to take the derivative of the numerator and of the denominator and evaluate the limit.




limx0+1x1x2=limx0+x=0


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