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Mathematics
Problem
For the real parameter
a
a
a
, consider the limit
L
(
a
)
=
lim
x
→
∞
2
x
2
a
+
5
x
3
a
−
7
\displaystyle L(a)=\lim_{x\to\infty}\dfrac{2x^{2a}+5}{x^{3a}-7}
L
(
a
)
=
x
→
∞
lim
x
3
a
−
7
2
x
2
a
+
5
. For which of the following sets of
a
a
a
does
L
(
a
)
L(a)
L
(
a
)
exist and equal
0
0
0
? a) All real
a
<
0
a<0
a
<
0
b)
a
=
0
a=0
a
=
0
only c) No real values of
a
a
a
d) All real
a
>
0
a>0
a
>
0
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