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Iran Contests
Iran MO (2nd Round)
1986 Iran MO (2nd round)
1
Find the limit of the function - [Iran Second Round 1986]
Find the limit of the function - [Iran Second Round 1986]
Source:
December 24, 2010
function
trigonometry
limit
algebra unsolved
algebra
Problem Statement
Let
f
f
f
be a function such that
f
(
x
)
=
(
x
2
−
2
x
+
1
)
sin
1
x
−
1
sin
π
x
.
f(x)=\frac{(x^2-2x+1) \sin \frac{1}{x-1}}{\sin \pi x}.
f
(
x
)
=
sin
π
x
(
x
2
−
2
x
+
1
)
sin
x
−
1
1
.
Find the limit of
f
f
f
in the point
x
0
=
1.
x_0=1.
x
0
=
1.
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