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Byju's Answer
Standard XII
Mathematics
Monotonically Decreasing Functions
If [ ] deno...
Question
If
[
]
denotes the greatest integer function
n
∈
N
, then
lim
x
→
0
[
n
sin
X
X
]
is equal to
A
n
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B
0
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C
n
−
1
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D
n
+
1
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Solution
The correct option is
D
n
−
1
sin
x
<
x
at
x
→
0
therefore
l
i
m
x
→
0
n
sin
x
x
=
n
−
1
this is because at neighbourhood of zero sinx/x is slightly less than 1.
Suggest Corrections
0
Similar questions
Q.
If
n
∈
N
,
and
[
x
]
denotes the greatest integer less than or equal to x, then
lim
x
→
n
(
−
1
)
[
x
]
is equal to
Q.
lim
x
→
0
−
∑
2
n
+
1
r
=
1
[
x
r
]
+
(
n
+
1
)
1
+
[
x
]
+
|
x
|
+
2
x
(
where
n
ϵ
N
&
[
.
]
denotes the greatest integer function
)
equals
Q.
If
lim
x
→
0
+
x
(
[
1
x
]
+
[
5
x
]
+
[
11
x
]
+
[
19
x
]
+
[
29
x
]
+
.
.
.
.
.
.
.
t
o
n
t
e
r
m
s
)
=
430
(where [.] denotes the greatest integer function), then
n
=
Q.
The value of integral
∞
∫
0
[
n
⋅
e
−
x
]
d
x
is equal to
(
where
[
⋅
]
denotes the greatest integer function and
n
∈
N
,
n
>
1
)
Q.
Consider the following statements:
S
1
:
lim
x
→
0
−
[
x
]
x
is an indeterminate from (where [.] denotes greatest integer function).
S
2
:
lim
x
→
∞
sin
(
3
x
)
3
x
=
0
S
3
:
lim
x
→
∞
√
x
−
sin
x
x
+
cos
2
x
does not exist.
S
4
:
lim
n
→
∞
(
n
+
2
)
!
+
(
n
+
1
)
!
(
n
+
3
)
!
(
n
∈
N
)
=
0
Which of the statements
S
1
,
S
2
,
S
3
,
S
4
are true or false:
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