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Byju's Answer
Standard XII
Mathematics
Graphical Interpretation of Differentiability
lf fx=[ ...
Question
lf
f
(
x
)
=
{
1
,
x
<
0
1
+
s
i
n
x
,
0
≤
x
<
/
Ï€
2
, then derivative of f(x) at
x
=
0
A
is equal to 1
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B
is equal to 0
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C
is equal to -1
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D
does not exist
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Solution
The correct option is
D
does not exist
LHD at x=0
=
[
d
d
x
1
]
x
=
0
=
0
RHD at x=0
=
[
d
d
x
1
+
sin
x
]
x
=
0
=
c
o
s
0
=
1
hence
f
′
doesn't exist
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0
Similar questions
Q.
lf
f
(
x
)
=
x
,
x
<
0
;
f
(
x
)
=
0
,
x
=
0
;
f
(
x
)
=
x
2
;
x
>
0
, then
lim
x
→
0
f
(
x
)
is equal to
Q.
Let
f
(
x
)
=
{
e
x
2
+
x
,
x
<
0
a
x
+
b
x
≥
0
. Then
f
(
x
)
is continuous and has a derivative at
x
=
0
,
for
(
a
,
b
)
equal to:
Q.
If
f
(
x
)
=
1
for
x
<
0
=
1
+
sin
x
for
0
≤
x
<
π
/
2
,
then at x=0, then show that the derivative
f
′
(
x
)
does not exist.
Q.
lf
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
−
1
,
x
<
0
0
,
x
=
0
1
,
x
>
0
and
g
(
x
)
=
sin
x
+
cos
x
, then points of discontinuity of
(
f
o
g
)
(
x
)
in
(
0
,
2
π
)
are
Q.
lf
f
(
x
)
=
lim
n
→
∞
n
2
(
x
1
/
n
−
x
1
/
(
n
+
1
)
)
,
x
>
0
, then
∫
x
f
(
x
)
d
x
is equal to
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