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

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SUMMARY

The limit of x^x as x approaches 0 is definitively 1. This conclusion can be reached by rewriting x^x as exp(log(x)/(1/x)). While this proves the limit, it does not establish that 0^0 equals 1 or address the uniqueness of 0^0 as the limit of x^y when both x and y approach 0. The discussion highlights the importance of understanding exponential and logarithmic functions in calculus.

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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?
 
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hint: ask yourself what x to the 0 power is.
 
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hint write
x^x=exp(log(x)/(1/x))
 
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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.
 
http://pokit.etf.ba/get/e57018aced28181afefff3a8e5a3e402.jpg

there you go, njoy
 
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thank you very much, I'm actually quite disappointed i can't think that creatively
 
I am first year electrical engineering, this is trivial for me, I have to know much more complicated things (: so don't be disappointed
 

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