Answers and Explanations 211
Now apply the limit:
= − +
= −
1
1 0
1
242.
∞
Divide the numerator and denominator by the highest power of x that appears in the
denominator, x
2
, and simplify:
lim
lim
lim
x
x
x
x
x
x
x
x
x
x
x
x
x
x
→−∞
→−∞
→−∞
+
−
+
=
+
−
+
=
8
3
5
1
8
3
5
1
8
4
2
4
2
2
2
2
2
2
x x
x x
x
2
2
2
3
5
1 1
+ −
+
Then apply the limit. Consider what happens in the numerator and the denominator as
x → –∞. In the numerator, 8
3
5
2
2
x
x x
+ −





 → ∞, and in the denominator, 1 1
1
2
+





 →
x
.
Therefore, you have
lim
x
x
x x
x
→−∞
+ −
+
= ∞
8
3
5
1 1
2
2
2
243.
−3
To simplify the expression underneath the radical, begin by multiplying the numerator
and denominator by 1
5
x
:
lim
lim
x
x
x
x
x
x
x
x
x
x
→−∞
→−∞
−
+
=
−
+
(
)
9
1
1 9
1
1
10
5
5
10
5
5
Answers
201–300