Friday, September 23, 2016

calculus - Deconstructing 00





It is well known that 00 is an indeterminate form. One way to see that is noticing that


limx0+0x=0,


yet,


limx0x0=1.


What if we make both terms go to 0, that is, how much is


L=limx0+xx?


By taking x1/kkN, I concluded that it equals limxx1/x, but that's not helpful.



Answer



This is, unfortunately, not very exciting. Rewrite xx as exlogx and take that limit. One l'Hôpital later, you get 1.


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