Math 116 CALCULUS II
MIDTERM EXAM – II (Takehome)
November 14 (Thu), 2013
Due date: November 19 (Tue), 2013
Seat # :
Instructor:
Yasuyuki Kachi
Line #:
23590.
ID # :
Name :
This takehome part of Midterm Exam II is worth 40 points, plus
extra 30 points, and is due in class Tuesday, November 19th, 2013.
Submission after 1:00 pm, November 19th will not be accepted.
•
Be sure to write your answers neatly, precisely, and with complete
sentences. You may use notes and handed out materials, but no outside
help.
•
Print oF one entire set of this exam. Write answers in the printed
sheets. You may not supply your own (blank) sheet except for [III].
[I] (Takehome; 10pts)
State the general Taylor’s formula
using the summation
symbol. It has two parts. One is concerning a Fnite sum and it involves an integral.
The other is concerning an inFnite sum.
(a)
f
(
x
)
=
m
s
n
=0
+
i
t
=
dt.
(b)
If
lim
m
→
∞
= 0,
then
f
(
x
)
=
∞
s
n
=0
.
1
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View Full Document[II] (Takehome; 10pts)
Madam Rich has recently received a letter from the
President and CEO of The University X, her alma mater. It goes:
Dear Madam Rich,
We are so pround of you as being the most prominent alumna of The University
X. Could you please help us by donating us some money.
We will proudly
name our new football stadium “Madam Rich Stadium”. Please agree to sign the
enclosed sheet. Sincerely yours,
***
, President
&
CEO of The University X
a
Enclosed sheet
A
I, Madam Rich, hereby agree to consecutively
pay to The University X, exactly
as dictated by the payment schedule below. I agree that, on each payment, the
amount will be automatically deducted from my bank account, with account
number xxx, and it will be automatically transferred to The University X account.
Payment Schedule
A.
The amount
of payment on the payment #
n
is exactly
one
n
th of a dollar
p
= $
1
n
P
.
(
See Table 1.
)
B.
As for the timing
of payments, the interval between two consecutive payments
is exactly one half of the previous interval.
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 Fall '08
 SCHOLLE,MINHO
 Calculus, Following, lim, Christopher Nolan, Madam Rich

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