Find lim as x-->0+ for x^(tan x).
It seems to suggest 0^0 = 1, but when I apply L'Hopital's I get 0 instead. Help would be great
edit: sorry missed out the minus sign, should be 0 instead of infinity.
There are many ways, but the easies would probably be
Let
So as
So we would have
Now we can say one of two things
Or
And
This implies that
Now remaining inequality
Now the left and right limits are obviously zero, so we have
This implies by the squeeze theorem that
And now finally seeing either that
If
Or more simply that
We can finally conclude that
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Hope that wasn't too formal for you