__________________________
____________________
________________
YOUR NAME
INSTRUCTOR’S NAME
SEC. #, TIME
Math 115a Final Examination
December 19, 2007
9AM – Noon
Some quotations from Yogi Berra:
"I made a wrong mistake."
“I wish I had an answer to that because I'm tired of answering that question.”
“If you ask me anything I don't know, I'm not going to answer.”
No books, notes, calculators, computers are allowed.
Trigonometric identities
: sin
sin cos ,
cos
cos
22
1
2
xx
x
x
x
==
−
For Parts A and B, write your answers on the exam sheet.
Part A: True or False (18 points)
For problems 19, please mark your answer as
True (T) or False (F)
clearly in the space
next to each problem. Each problem solved correctly gets 2 points, while each incorrect
answer gets zero points.
1. The series
1
n
n
e
π
∞
=
⎛⎞
⎜⎟
⎝⎠
∑
is convergent
.
YOUR ANSWER:
T
2.
0
sin
()
x
t
f
xd
t
t
=
∫
has a critical point at
x
=
.
YOUR ANSWER:
T
3. The power series
1
2
!
nn
n
x
n
∞
=
∑
is divergent for
1
2
x
>
. YOUR ANSWER:
F
4. If
0
n
a
>
and
1
n
n
a
∞
=
∑
converges
then
1
sin
n
n
a
∞
=
∑
also converges.
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 '08
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 Math, Taylor Series, dx

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