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Byju's Answer
Standard XII
Mathematics
Addition of Vectors
Let fx=1-|cos...
Question
Let
f
(
x
)
=
1
−
|
cos
x
|
∀
x
∈
R
,
then which among the following options is/are correct?
A
f
′
(
π
2
)
does not exist
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B
f
(
x
)
is continuous everywhere
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C
f
(
x
)
is not differentiable everywhere
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D
lim
x
→
π
2
+
f
(
x
)
=
1
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Solution
The correct option is
D
lim
x
→
π
2
+
f
(
x
)
=
1
f
(
x
)
=
1
−
|
cos
x
|
is continuous as
cos
x
is continuous for all
x
which gives
|
cos
x
|
is also continuous.
Hence,
1
−
|
cos
x
|
is continuous.
Also,
lim
x
→
π
2
+
f
(
x
)
=
lim
x
→
π
2
+
1
−
|
cos
x
|
=
1
Also, since
f
(
x
)
has sharp corner at
x
=
π
2
. Hence,
f
′
(
π
2
)
does not exist.
Similar sharp corners occur at all the points where
cos
x
=
0
i.e. at
x
=
(
2
n
+
1
)
π
2
,
n
∈
Z
.
Hence,
f
(
x
)
is not differentiable everywhere.
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0
Similar questions
Q.
Let
f
(
x
)
=
x
3
−
x
2
+
x
+
1
and
g
(
x
)
=
{
max
{
f
(
t
)
}
,
0
≤
t
≤
x
,
0
≤
x
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3
−
x
,
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2
,
Then which among the following options is/are correct for
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x
)
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,
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]
Q.
If
f
(
x
)
=
sin
−
1
(
cos
x
)
cos
−
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(
sin
x
)
∀
x
∈
[
0
,
2
π
]
,
then which of the following statement(s) is/are correct?
Q.
Let
f
and
g
be two differentiable functions such that
f
(
x
)
is odd and
g
(
x
)
is even. If
f
(
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)
=
7
,
f
(
0
)
=
0
,
g
(
x
)
=
f
(
x
+
5
)
and
f
(
x
)
=
x
∫
0
g
(
t
)
d
t
∀
x
∈
R
,
then which of the following is/are CORRECT?
Q.
f
(
x
)
=
min
{
cos
x
,
1
−
sin
x
}
,
−
π
≤
x
≤
π
.
Then which among the following options is/are correct
Q.
If a function
f
(
x
)
is defined as
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
−
x
,
x
<
0
x
2
,
0
≤
x
≤
1
x
2
−
x
+
1
,
x
>
1
,
then which among the following option is correct
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Addition of Vectors
Standard XII Mathematics
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