What Is the Limit of x^x as x Approaches 0?

[marshmellow]

Though I know that the limit as x approaches 0 of x^x is 1, I can't prove it...

...can anyone please help me?

 

[christopherV]

hint: ask yourself what x to the 0 power is.

 

[lurflurf]

hint write
x^x=exp(log(x)/(1/x))

 

[JJacquelin]

Hello marshmellow
certainly you will succeed in proving that the limit for x^x is 1 while x tends to 0.
But remember, this doesn't prove that 0^0 = 1 and most certainly not the uniqueness of 0^0 as limit of x^y while both x and y tend to 0.

 

[Bassalisk]

http://pokit.etf.ba/get/e57018aced28181afefff3a8e5a3e402.jpg

there you go, njoy

 

[marshmellow]

thank you very much, I'm actually quite disappointed i can't think that creatively

 

[Bassalisk]

I am first year electrical engineering, this is trivial for me, I have to know much more complicated things (: so don't be disappointed