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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
a
x
+
2
,
x
<
2
6
,
x
>
2
f(x)=\begin{cases}ax+2,& x<2\\6,& x>2\end{cases}
f
(
x
)
=
{
a
x
+
2
,
6
,
x
<
2
x
>
2
and define
F
(
x
)
=
10
+
∫
1
x
f
(
t
)
d
t
F(x)=10+\int_{1}^{x} f(t)\,dt
F
(
x
)
=
10
+
∫
1
x
f
(
t
)
d
t
. Determine the value of
a
a
a
for which
F
F
F
is differentiable at
x
=
2
x=2
x
=
2
.
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