Evaluate the limit (x^4-16)/(x-2), x-->2.

limit (x^4-16)/(x-2),
x-->2.

First we will try substituting to find the
limit.

We will substitute with x=
2:

==> lim (x^4 - 16) / (x-2) =
0/0

==> Now we will factor the
numerator:

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

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

Now we will reduce
similar:

==> lim (x+2)(x^2+4)  x-->
2

Now substitute with x=2:

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

                                  =
4*8 = 32

Then, lim (x^4-16)/(x-2) when x--> 2
is 32.