What is 0^0 equals to?
a.1
b.0
c.undefine
7 answers
It is defined as zero.
but my calculator says 1 and isn't all numbers raised to zero is equal to 1?
Help! It's very confusing...
Help! It's very confusing...
Get a new calculator. O to any power is zero, by definition. Technically, O^0 is undefined, because the term x^y as a function of two variables is undefined at the origin.
0^0 is undefined
reason:
0^n = 0 for any value of n
but a^0 = 1 for any value of a
so we have a contradiction, which drives mathematicians crazy, thus it is undefined
my 25 year old calculator gives me an error message for 0^0
reason:
0^n = 0 for any value of n
but a^0 = 1 for any value of a
so we have a contradiction, which drives mathematicians crazy, thus it is undefined
my 25 year old calculator gives me an error message for 0^0
However, if you look at the graph for
y = x^x
the limit near zero is 1.
limit x^x
log(limit) = x*logx
= logx/(1/x)
use l'Hospital's rule:
= (1/x) / (-1/x^2)
= -x
log(limit)=0, so limit=1
y = x^x
the limit near zero is 1.
limit x^x
log(limit) = x*logx
= logx/(1/x)
use l'Hospital's rule:
= (1/x) / (-1/x^2)
= -x
log(limit)=0, so limit=1
My two year old calculator gives an answer of "invalid".
thanks for your answers...
I can now explain the different answers to my professor..
I can now explain the different answers to my professor..
1 answer