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Byju's Answer
Standard XII
Mathematics
Inverse of a Function
limx→ 1-x+x-[...
Question
lim
x
→
1
−
{
x
+
(
x
−
[
x
]
)
2
}
=
(
[
x
]
is greatest integer function)
A
−
1
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B
0
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C
2
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D
does not exist
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Solution
The correct option is
D
2
When x
→
1
−
0
<
x
<
1
O
r
,
[
x
]
=
0
Hence, substitute limit,
(
l
i
m
x
→
1
−
x
)
+
l
i
m
x
→
1
−
(
x
−
[
x
]
)
2
=
1
+
(
1
−
0
)
2
=
2
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0
Similar questions
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
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/
x
+
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)
does not exists.
Q.
A function
f
:
R
→
R
+
satisfying
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
∀
x
,
y
∈
R
,
f
(
0
)
=
1
,
f
′
(
0
)
=
2
, then
Q.
lim
x
→
0
[
x
]
x
does not exist as the function is not defined at
x
=
0
, where
[
.
]
denotes greatest integer function.
If true enter 1, else enter 0.
Q.
Statement
I
:
lim
x
→
0
[
x
]
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
e
1
x
−
1
e
1
x
+
1
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
(where [.] represents the greatest integer function) does not exist
Statement
I
I
:
lim
x
→
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⎛
⎜ ⎜ ⎜
⎝
e
1
x
−
1
e
1
x
+
1
⎞
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⎠
does not exist
Q.
lim
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→
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(a) 1 (b) 2 (c) 0 (d) does not exist
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