Answer: lim
x
→
2
x
2
−
4
x
−
2
=
4
Step-by-step explanation: If we look at the graph of
y
=
x
2
−
4
x
−
2
we can see that it is clear that the limit exists, and is approximately
4
graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}
The numerator is the difference of two squares, and as such we can factorise using it as
A
2
−
B
2
≡
(
A
+
B
)
(
A
−
B
)
Se we can factorise as follows:
lim
x
→
2
x
2
−
4
x
−
2
=
lim
x
→
2
x
2
−
2
2
x
−
2
=
lim
x
→
2
(
x
+
2
)
(
x
−
2
)
x
−
2
=
lim
x
→
2
(
x
+
2
)
x
−
2
x
−
2
=
lim
x
→
2
(
x
+
2
)
=
(
2
+
2
)
=
4