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South Korea USCM
2016 Korea USCM
5
infty norm and -infty norm
infty norm and -infty norm
Source: 2016 South Korea USCM P5
August 16, 2020
real analysis
Lp norm
limits
college contests
function
Problem Statement
For
f
(
x
)
=
cos
(
3
3
π
8
(
x
−
x
3
)
)
f(x) = \cos\left(\frac{3\sqrt{3}\pi}{8}(x-x^3 ) \right)
f
(
x
)
=
cos
(
8
3
3
π
(
x
−
x
3
)
)
, find the value of
lim
t
→
∞
(
∫
0
1
f
(
x
)
t
d
x
)
1
t
+
lim
t
→
−
∞
(
∫
0
1
f
(
x
)
t
d
x
)
1
t
\lim_{t\to\infty} \left( \int_0^1 f(x)^t dx \right)^\frac{1}{t} + \lim_{t\to-\infty} \left( \int_0^1 f(x)^t dx \right)^\frac{1}{t}
t
→
∞
lim
(
∫
0
1
f
(
x
)
t
d
x
)
t
1
+
t
→
−
∞
lim
(
∫
0
1
f
(
x
)
t
d
x
)
t
1
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