Math 116 CALCULUS II
PRACTICE EXAM – FINAL B (For InClass)
December 5 (Thu), 2013
Seat # :
Instructor:
Yasuyuki Kachi
Line #:
23590.
ID # :
Name :
⋆
This is ‘Version B’ of the practice exam. (There are ‘Versions A,C’.)
The actual exam may not be very similar to these practice exams. The
purpose of these practice exams is to give you an idea of how the actual
exam will look like, in terms of the length and the format. This practice
exam is for the “inclass” portion of the exam only.
[I] (30pts)
Let
J
(
x
)
be defned over the interval
p
 ∞
,
+
∞
P
. Assume
J
(
0
)
= 1
and moreover that For an arbitrary positive integer
ℓ
J
(2
ℓ

1)
(
0
)
= 0,
J
(2
ℓ
)
(
0
)
=
p

1
P
ℓ
p
2
ℓ

1
P
! !
p
2
ℓ
P
! !
.
(1)
J
(1)
(
0
)
= 0,
J
(2)
(
0
)
=

1
!!
2
!!
,
J
(3)
(
0
)
= 0,
J
(4)
(
0
)
=
3
!!
4
!!
,
J
(5)
(
0
)
= 0,
J
(6)
(
0
)
=

!!
!!
,
J
(7)
(
0
)
= 0,
J
(8)
(
0
)
=
!!
!!
,
·
·
·
·
·
·
1
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([I] continued)
(2)
Use the general Taylor’s formula to write out the Taylor series for
J
(
x
)
:
(2a)
J
(
x
)
=
∞
s
ℓ
=0
·
x
2
ℓ
.
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 Fall '08
 SCHOLLE,MINHO
 Calculus, Power Series, Taylor Series, Taylor series expression

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