Answer
a. $1$, see table.
b. $1$, see graph.
Work Step by Step
a. See table for the calculations; we can see that:
as $x\to0$, $y\to1$.
b. See graph; it can be seen that the function approaches the y-axis to a value of $y=1$
Extra: prove analytically. Given $y=x^x$, we have $x=\log_xy=\ln(y)/\ln(x)$, thus $\ln(y)=x\cdot \ln(x)=\ln(x)/(1/x)$ and using L’Hopital’s Rule, we have $\lim_{x\to0} \ln(y) =\lim_{x\to0} \ln x/(1/x)=\lim_{x\to0}(1/x)/(-1/x^2)= \lim_{x\to0}(-x)=0$ which gives $y=1$
