Question :

let $\displaystyle h(x)=x^2, x<2$

$\displaystyle = 3, x=2$

$\displaystyle =2, x>2$

Show that

lim(x-->2)h(x)does not equal to 4

my teacher give the answer :

for $\displaystyle 2<x<2+delta => h(x) = 2 => abs(h(x)-4)=2$

Thus for $\displaystyle epsilon < 2, abs(h(x)-4) >= epsilon $ whenever $\displaystyle 2<x<2+delta$ no matter how small we choose

$\displaystyle delta > 0$ => lim(x-->2)h(x)does not equal to 4

i cannot understand the second line of the explanation. why we have to consider $\displaystyle epsilon < 2 $

why cannot consider this : $\displaystyle abs(h(x)-4)=2 < epsilon $ thus, $\displaystyle epsilon should > 2 $ right?

can anyone explain it to me? i really could'nt understand this!