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Mathematics
Mathematics
Problem
Consider the limit
lim
x
→
∞
(
k
−
3
)
x
4
+
2
x
2
(
k
+
1
)
x
4
−
5
x
3
.
\lim_{x\to\infty}\frac{(k-3)x^{4}+2x^{2}}{(k+1)x^{4}-5x^{3}}.
x
→
∞
lim
(
k
+
1
)
x
4
−
5
x
3
(
k
−
3
)
x
4
+
2
x
2
.
For which value of
k
k
k
does the limit exist and equal
0
0
0
? a)
k
=
−
1
k=-1
k
=
−
1
b)
k
=
3
k=3
k
=
3
c)
k
=
−
2
k=-2
k
=
−
2
d)
k
=
0
k=0
k
=
0
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