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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
a
x
3
+
b
x
2
+
1
x
2
+
3
g(x)=\dfrac{ax^{3}+bx^{2}+1}{x^{2}+3}
g
(
x
)
=
x
2
+
3
a
x
3
+
b
x
2
+
1
. For which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
does
lim
x
→
∞
g
(
x
)
\displaystyle \lim_{x\to\infty} g(x)
x
→
∞
lim
g
(
x
)
exist and equal
6
6
6
? a)
(
6
,
0
)
(6,0)
(
6
,
0
)
b)
(
6
,
6
)
(6,6)
(
6
,
6
)
c)
(
0
,
6
)
(0,6)
(
0
,
6
)
d)
(
0
,
−
6
)
(0,-6)
(
0
,
−
6
)
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