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Byju's Answer
Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
What is lim...
Question
What is
lim
x
→
0
x
2
sin
(
1
x
)
equal to ?
A
0
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B
1
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C
1/2
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D
Limit does not exist.
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Solution
The correct option is
A
0
lim
x
→
0
x
2
sin
(
1
x
)
=
0
2
×
sin
(
1
0
)
[
−
1
≤
sin
(
1
x
)
≤
1
]
=
0
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0
Similar questions
Q.
Assertion :If
lim
x
→
0
{
f
(
x
)
+
sin
x
x
}
does not exist, then
lim
x
→
0
f
(
x
)
does not exist. Reason:
lim
x
→
0
sin
x
x
exists and has value 1.
Q.
Assertion :
lim
x
→
0
e
1
/
x
−
1
e
1
/
x
+
1
does not exist. Reason:
lim
x
→
0
+
e
1
/
x
−
1
e
1
/
x
+
1
does not exist.
Q.
lim
x
→
∞
|
x
|
x
is equal to
Q.
STATEMENT-1 :
lim
x
→
0
[
x
]
{
e
1
/
x
−
1
e
1
/
x
+
1
}
(where [.] represents the greatest integer function) does not exist.
STATEMENT-2 :
lim
x
→
0
(
e
1
/
x
−
1
e
1
/
x
+
1
)
does not exists.
Q.
Let
f
(
x
)
=
x
3
{
√
x
2
+
√
x
4
+
1
−
x
√
2
}
. Then
l
i
m
x
→
∞
f
(
x
)
is equal to
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