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) About Me  (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



So



Use the chain rule for limits:

If and and is continuous at then

Let and



Indeterminate form. Rewrite to a L'Hôpital form.



Apply L'Hôpital



Then



So by the chain rule



John

My calculator said it, I believe it, that settles it