We graph *f*: In order for the limit to exist we need both one-sided limits to exist.
As *x* approaches zero from the left, *y* gets close to 0 also, therefore
\lim_x\to 0^-*f*(*x*) = 0.
As *x* approaches zero from the right, *y* gets close to 1, therefore
\lim_x\to 0^ + *f*(*x*) = 1.
Since the left-side limit is 0 and the right-side limit is 1, and 0 and 1 aren't the same, therefore
\lim_x\to 0*f*(*x*)
does not exist. | |