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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
1984 Iran MO (2nd round)
2
2
Part of
1984 Iran MO (2nd round)
Problems
(1)
Find the period - [Iran Second Round 1984]
Source:
12/30/2010
Consider the function
f
(
x
)
=
sin
(
π
2
⌊
x
⌋
)
.
f(x)= \sin \biggl( \frac{\pi}{2} \lfloor x \rfloor \biggr).
f
(
x
)
=
sin
(
2
π
⌊
x
⌋
)
.
Find the period of
f
f
f
and sketch diagram of
f
f
f
in one period. Also prove that
lim
x
→
1
f
(
x
)
\lim_{x \to 1} f(x)
lim
x
→
1
f
(
x
)
does not exist.
function
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algebra