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Mathematics
Mathematics
Problem
A cubic polynomial
p
(
x
)
=
1
+
x
+
A
x
3
p(x)=1+x+Ax^{3}
p
(
x
)
=
1
+
x
+
A
x
3
is used to approximate
e
x
e^{x}
e
x
near
x
=
0
x=0
x
=
0
. Find the value of
A
A
A
that makes the third derivative of
p
p
p
equal to the third derivative of
e
x
e^{x}
e
x
at
x
=
0
x=0
x
=
0
.
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