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Byju's Answer
Standard XIII
Mathematics
Existence of Limit
x→ 1limx sin ...
Question
lim
x
→
1
x
sin
{
x
}
x
−
1
,
where {x} denotes the fractional part of x, is equal to
A
−
1
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B
0
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C
1
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D
does not exist
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Solution
The correct option is
D
does not exist
lim
x
→
1
−
0
{
x
}
=
lim
x
→
1
−
0
(
x
−
[
x
]
)
= 1-0=1
lim
x
→
1
+
0
{
x
}
=
lim
x
→
1
+
0
(
x
−
[
x
]
)
= 1-1=0
∴
lim
x
→
1
−
0
x
sin
{
x
}
x
−
1
=
lim
x
→
1
−
0
sin
{
x
}
=
−
∞
lim
x
→
1
+
0
x
sin
{
x
}
{
x
}
x
−
1
x
−
1
=
1
×
1
×
1
=
1
Since, L.H. limit
≠
R.H. limit Limit does not exist.
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0
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→
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{
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−
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,
where {x} denotes the fractional part of x, is equal to
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