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Putnam
1974 Putnam
B2
Putnam 1974 B2
Putnam 1974 B2
Source: Putnam 1974
May 28, 2022
Putnam
continuous and differentiable
Problem Statement
Let
y
(
x
)
y(x)
y
(
x
)
be a continuously differentiable real-valued function of a real variable
x
x
x
. Show that if
y
′
(
x
)
2
+
y
(
x
)
3
→
0
y'(x)^2 +y(x)^3 \to 0
y
′
(
x
)
2
+
y
(
x
)
3
→
0
as
x
→
∞
,
x\to \infty,
x
→
∞
,
then
y
(
x
)
y(x)
y
(
x
)
and
y
′
(
x
)
→
0
y'(x) \to 0
y
′
(
x
)
→
0
as
x
→
∞
.
x \to \infty.
x
→
∞.
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