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IMC
1994 IMC
2
IMC 1994 D1 P2
IMC 1994 D1 P2
Source:
March 6, 2017
IMC
real analysis
Problem Statement
Let
f
∈
C
1
(
a
,
b
)
f\in C^1(a,b)
f
∈
C
1
(
a
,
b
)
,
lim
x
→
a
+
f
(
x
)
=
∞
\lim_{x\to a^+}f(x)=\infty
lim
x
→
a
+
f
(
x
)
=
∞
,
lim
x
→
b
−
f
(
x
)
=
−
∞
\lim_{x\to b^-}f(x)=-\infty
lim
x
→
b
−
f
(
x
)
=
−
∞
and
f
′
(
x
)
+
f
2
(
x
)
≥
−
1
f'(x)+f^2(x)\geq -1
f
′
(
x
)
+
f
2
(
x
)
≥
−
1
for
x
∈
(
a
,
b
)
x\in (a,b)
x
∈
(
a
,
b
)
. Prove that
b
−
a
≥
π
b-a\geq\pi
b
−
a
≥
π
and give an example where
b
−
a
=
π
b-a=\pi
b
−
a
=
π
.
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