Asked by Lori

lim x->0 (sinx)^x

Answers

Answered by Reiny
lim (sinx)^x , as x -->0
= 1
Answered by Lori
would it be possible to get the steps? or some sort of explanation?
Answered by Reiny
I used an intuitive approach.
as x --> 0 , sinx ---> 0 ,but not quite
anything raised to the zero is 1
(except 0^0 is undefined)

try this on your calculator ....
set it to radians
take sin(.000001)^.000001 to get .999986184
take sin(.00000001)^.00000001 to get .999999815
the closer we get to zero, the closer the result gets to 1
Answered by Lori
thank you!
Answered by Steve
or, take log:
ln(limit) = x * ln(sin x)
If t = 1/x, we have
ln(sin 1/t) / t
Now take derivatives a couple of times and you wind up with
ln(limit) = 0, so
limit = 1
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