Finding the Value of a Limit
Prequisite Knowledge
Problem
What is the value of the following limit:
lim
x
→ 2
x
2
− 25
x
− 5
Solution
Solve by factoring.
lim
x
→ 2
x
2
− 25
x
− 5
=
lim
x
→ 2
(
x
+ 5)(
x
− 5)
x
− 5
(
x
− 5) on top and bottom cancel each other.
=
lim
x
→ 2
(
x
+ 5)
Substitute 2 in for
x
, then:
lim
x
→ 2
x
2
− 25
x
− 5
= 7