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Mathematics
Mathematics
Problem
Let
g
(
t
)
=
{
t
2
,
t
≤
0
,
2
t
,
t
>
0
,
g(t)=\begin{cases}t^{2}, & t\le 0,\\2t, & t>0,\end{cases}
g
(
t
)
=
{
t
2
,
2
t
,
t
≤
0
,
t
>
0
,
and define
p
(
x
)
=
∫
x
sin
x
g
(
t
)
d
t
p(x)=\displaystyle\int_{x}^{\sin x} g(t)\,dt
p
(
x
)
=
∫
x
s
i
n
x
g
(
t
)
d
t
. Given that
g
(
0
)
=
0
g(0)=0
g
(
0
)
=
0
, what is
p
′
(
0
)
p'(0)
p
′
(
0
)
? a)
2
2
2
b)
−
2
-2
−
2
c)
0
0
0
d)
p
′
(
0
)
is undefined
p'(0)\text{ is undefined}
p
′
(
0
)
is undefined
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