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Mathematics
Problem
Let
k
k
k
be a non-zero real number. (a) Evaluate
L
=
lim
x
→
∞
x
3
+
k
x
2
+
1
k
x
3
−
5
.
L=\lim_{x\to\infty}\frac{x^{3}+k x^{2}+1}{k x^{3}-5}.
L
=
x
→
∞
lim
k
x
3
−
5
x
3
+
k
x
2
+
1
.
(b) Hence find the value of
k
k
k
for which
L
=
2
L=2
L
=
2
. a. Evaluate the limit
L
L
L
in terms of
k
k
k
. b. Find the value of
k
k
k
for which
L
=
2
L=2
L
=
2
.
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