Monday, 5 December 2016

limits - Why doesn't L'hopitals Rule work for limlimitsxtoinftyfracx+sinxx+2sinx?

This is how I would evaluate limxx+sinxx+2sinx



=limxx(1+sinxx)x(1+2sinxx)



=1+01+20=1



But now applying L'hopitals Rule, I get




limx1+cosx1+2cosx



Since cosx just oscillates between [1,1] I think we can conclude the limit doesn't exist.



What is going on here?

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