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1979 VTRMC
4
1979 VTRMC #4
1979 VTRMC #4
Source:
August 8, 2018
real analysis
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be continuously differentiable on
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
and suppose
lim
x
→
∞
f
′
(
x
)
=
0
\lim _ { x \rightarrow \infty } f ^ { \prime } ( x ) = 0
lim
x
→
∞
f
′
(
x
)
=
0
. Prove that
lim
x
→
∞
f
(
x
)
/
x
=
0
\lim _ { x \rightarrow \infty } f ( x ) / x = 0
lim
x
→
∞
f
(
x
)
/
x
=
0
.
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