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01.07.1
Multiple-Choice Test
Chapter 01.07
Taylors Series Revisited
1.
The coefficient of the
5
x
term in the Maclaurin polynomial for
( )
x
2
sin
is
(A)
0
(B)
0.0083333
(C)
0.016667
(D)
0.26667
2.
Given
( )
6
3
=
f
,
( )
8
3
=
′
f
,
( )
11
3
=
′
′
f
, and that all other higher order derivatives of
( )
x
f
are zero at
3
=
x
, and assuming the function and all its derivatives exist and are
continuous between
3
=
x
and
7
=
x
, the value of
( )
7
f
is
(A)
38.000
(B)
79.500
(C)
126.00
(D)
331.50
3.
Given that
( )
x
y
is the solution to
2
3
+
=
y
dx
dy
,
3
)
0
(
=
y
the value of
( )
2
.
0
y
from a
second order Taylor polynomial written around
0
=
x
is
(A)
4.400
(B)
8.800
(C)
24.46
(D)
29.00
4.
The series
( )
∑
∞
=
−
0
2
4
)!
2
(
1
n
n
n
n
n
x
is a Maclaurin series for the following function
(A)
( )
x
cos
(B)
( )
x
2
cos
(C)
( )
x
sin
(D)
( )
x
2
sin

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