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2014 BMT Spring
9
2014 BMT Team 9 limit
2014 BMT Team 9 limit
Source:
January 6, 2022
calculus
Problem Statement
Two different functions
f
,
g
f, g
f
,
g
of
x
x
x
are selected from the set of real-valued functions
{
s
i
n
x
,
e
−
x
,
x
ln
x
,
arctan
x
,
x
2
+
x
−
x
2
+
x
−
x
,
1
x
}
\left \{sin x, e^{-x}, x \ln x, \arctan x, \sqrt{x^2 + x} -\sqrt{x^2 + x} -x, \frac{1}{x} \right \}
{
s
in
x
,
e
−
x
,
x
ln
x
,
arctan
x
,
x
2
+
x
−
x
2
+
x
−
x
,
x
1
}
to create a product function
f
(
x
)
g
(
x
)
f(x)g(x)
f
(
x
)
g
(
x
)
. For how many such products is
lim
x
→
i
n
f
t
y
f
(
x
)
g
(
x
)
\lim_{x\to infty} f(x)g(x)
lim
x
→
in
f
t
y
f
(
x
)
g
(
x
)
finite?
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