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Mathematics
Mathematics
Problem
Let
P
(
x
)
=
a
m
x
m
+
…
P(x)=a_m x^m+\dots
P
(
x
)
=
a
m
x
m
+
…
and
Q
(
x
)
=
b
n
x
n
+
…
Q(x)=b_n x^n+\dots
Q
(
x
)
=
b
n
x
n
+
…
with
a
m
,
b
n
≠
0
a_m,b_n\neq 0
a
m
,
b
n
=
0
. State the relation between
m
m
m
and
n
n
n
that ensures
lim
x
→
∞
P
(
x
)
Q
(
x
)
=
0
\displaystyle\lim_{x\to\infty}\frac{P(x)}{Q(x)}=0
x
→
∞
lim
Q
(
x
)
P
(
x
)
=
0
.
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