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Mathematics
Mathematics
Problem
The left hand derivative of
f
(
x
)
=
⌊
x
⌋
sin
(
π
x
)
f(x) = \lfloor x\rfloor \sin(\pi x)
f
(
x
)
=
⌊
x
⌋
sin
(
π
x
)
at
x
=
k
x = k
x
=
k
, where
k
k
k
is an integer, is a.
(
−
1
)
k
(
k
−
1
)
π
(-1)^k (k-1) \pi
(
−
1
)
k
(
k
−
1
)
π
b.
(
−
1
)
k
−
1
(
k
−
1
)
π
(-1)^{k-1} (k-1) \pi
(
−
1
)
k
−
1
(
k
−
1
)
π
c.
(
−
1
)
k
π
(-1)^k \pi
(
−
1
)
k
π
d.
(
−
1
)
k
−
1
π
(-1)^{k-1} \pi
(
−
1
)
k
−
1
π
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