Part II: The Answers
212
Because x is approaching –∞, you know that x < 0. So as you take the limit, you need to
use the substitution 1
1
5
1 0
x
x
= −
in the numerator:
lim
lim
lim
x
x
x
x
x
x
x
x
x
x
x
x
x
x
→−∞
→−∞
→
−
+
(
)
=
−
−
+
=
1 9
1
1
1 9
1
5
10
5
5
10
10
5
5
5
− −∞
→−∞
−
−
+
=
− −
+
9
1 1
9 1
1 1
10
10
10
5
9
5
x
x
x
x
x
x
x
x
lim
Now apply the limit:
= − −
+
= −
9 0
1 0
3
244.
3
To simplify the expression underneath the radical, begin by multiplying the numerator
and denominator by 1
5
x
:
lim
lim
lim
x
x
x
x
x
x
x
x
x
x
x
x
x
x
→∞
→∞
→∞
−
+
=
−
+
(
)
=
−
9
1
1 9
1
1
1 9
10
5
5
10
5
5
10
10
x x
x
x
x
x
x
x
x
x
x
x
x
5
5
5
10
10
10
5
9
5
1
9
1 1
9 1
1 1
+
=
−
+
=
−
+
→∞
→∞
lim
lim
Now apply the limit:
=
−
+
=
9 0
1 0
3
Answers
201–300