Question :

let

Show that

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

my teacher give the answer :

for

Thus for whenever no matter how small we choose

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

i cannot understand the second line of the explanation. why we have to consider

why cannot consider this : thus, right?

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