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Mathematics
Mathematics
Problem
Let
k
k
k
be a real constant. Examine the limit
L
=
lim
x
→
∞
4
x
3
+
6
x
+
k
2
x
3
−
5
.
L=\lim_{x\to\infty}\frac{4x^{3}+6x+k}{2x^{3}-5}.
L
=
x
→
∞
lim
2
x
3
−
5
4
x
3
+
6
x
+
k
.
(a) Determine the condition on
k
k
k
for which the limit
L
L
L
exists and is finite. (b) For the value(s) of
k
k
k
found in part (a), evaluate
L
L
L
.
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