Sunday, 30 June 2019

calculus - A limit without using L'hoptial's rule

Define the natural number e by e=limx0(1+x)1/x.



Then, I can prove limx0ex1x=1.




Let z=ex1. Then, x=ln(z+1) and limx0ex1x=limz0zln(z+1)=1lne=1.



Using a similar trick (without L'Hoptial's rule), can we prove limx0ex1xx2=12?

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