SOLUTION: Limit x approch to zero X^x=.............
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Question 1082790: Limit x approch to zero X^x=.............
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You wrote:
)
Which is trivial and equal to 1 since I have to assume that 
is a constant.
On the other hand, if what you really meant was:
)
which, coincidentally, has the same answer but the solution is far from trivial.
Use
}\ =\ e^{x\ln(a)})
So
})
Use the chain rule for limits:
If \ =\ L)
and \ =\ b)
and )
is continuous at 
then \right)\ =\ L)
Let \ =\ x\ln(x))
and \ =\ e^u)
\right))
Indeterminate form. Rewrite to a L'Hôpital form.
}{\frac{1}{x}\right))
Apply L'Hôpital
\ =\ \lim_{x\rightarrow0}(-x)\ =\ 0)
Then
\ =\ e^0\ =\ 1)
So by the chain rule
\ =\ 1)
John
My calculator said it, I believe it, that settles it
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