Answer
1
Work Step by Step
We have to compute $\lim\limits_{x \to 0} x^x$.
We use a calculator to evaluate the function $f(x)=x^x$ for values of $x$ very close to 0.
Let $x_1=0.000001,x_2=0.0000001, x_3=0.00000001$.
$f(x_1)=f(0.000001)=0.000001^{0.000001}=0.999986184585$
$f(x_2)=f(0.0000001)=0.0000001^{0.0000001}=0.999998388192$
$f(x_3)=f(0.00000001)=0.00000001^{0.00000001}=0.999999815793$
Therefore we have:
$\lim\limits_{x \to 0} x^x=1$
