What is the value for lim x-->2 [ (x^3 -8) / (x^2 -4)]

We see that if x is replced by 2 in (x^3 -8) / (x^2 -4) we
get 0/0 which cannot be determined.

Instead we first
factorize the numerator and denominator and cancel the common terms, this
gives

[ (x^3 -8) / (x^2 -4)]
=>

[ (x-2) ( x^2 + 2x +4) ] / [(x-2) (
x+2)

=> (x^2 +2x +4) /
(x+2)

Now lim x--> 2 [(x^2 +2x +4) /
(x+2)]

=> (2^2 +2*2 + 4) /
(2+2)

=> (4+4+4) / 4 =>
3

Therefore lim x-->2 [ (x^3 -8) /
(x^2 -4)] = 3