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Byju's Answer
Standard XI
Mathematics
Left Hand Derivative
The left-hand...
Question
The left-hand derivative
of
f
(
x
)
=
[
x
]
s
i
n
(
π
x
)
at x= k, k
is an integer and
[x]
= greatest integer
,
is
A
(
−
1
)
k
(
k
−
1
)
π
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B
(
−
1
)
k
−
1
(
k
−
1
)
π
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C
(
−
1
)
k
k
π
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D
(
−
1
)
k
−
1
k
π
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Solution
The correct option is
A
(
−
1
)
k
(
k
−
1
)
π
f
′
(
k
−
0
)
=
lim
h
→
0
[
k
−
h
]
s
i
n
π
(
k
−
h
)
−
[
k
]
s
i
n
π
k
−
h
=
lim
h
→
0
(
−
1
)
k
−
1
(
k
−
1
)
s
i
n
π
h
−
k
×
0
−
h
=
lim
h
→
0
(
−
1
)
k
−
1
(
k
−
1
)
s
i
n
π
h
−
h
=
(
−
1
)
k
.
(
k
−
1
)
π
Suggest Corrections
3
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