It is well known that 00 is an indeterminate form. One way to see that is noticing that
limx→0+0x=0,
yet,
limx→0x0=1.
What if we make both terms go to 0, that is, how much is
L=limx→0+xx?
By taking x∈⟨1/k⟩k∈N∗, I concluded that it equals limx→∞x−1/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.
No comments:
Post a Comment