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Mathematics
Problem
Which of the following gives the Lagrange remainder when the fourth-degree Maclaurin polynomial is used to approximate
e
x
e^{x}
e
x
at
x
=
0.5
x=0.5
x
=
0.5
? (Here
c
c
c
is a number between
0
0
0
and
0.5
0.5
0.5
.) a)
e
c
(
0.5
)
4
4
!
\dfrac{e^{c}\,(0.5)^{4}}{4!}
4
!
e
c
(
0.5
)
4
b)
e
c
(
0.5
)
5
5
!
\dfrac{e^{c}\,(0.5)^{5}}{5!}
5
!
e
c
(
0.5
)
5
c)
e
0.5
(
0.5
)
5
5
!
\dfrac{e^{0.5}\,(0.5)^{5}}{5!}
5
!
e
0.5
(
0.5
)
5
d)
e
c
(
0.5
)
5
4
!
\dfrac{e^{c}\,(0.5)^{5}}{4!}
4
!
e
c
(
0.5
)
5
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