Spring 2011: MATH 1220-004
Wed. 20th April
Calculus II
Dr. F?. Lodh
Midterm Examination
50 minutes
Name:
Student ID:
Instructions.
1. Attempt all questions.
2. The examiner values clear writing, neat presentation. ai~d logical arguments.
3. No calculators or cheat sheets allowed.
4. Scratch paper is on the last page. Ask tile instructor if you need some more.
~__Question
Points Your Score
Q~
20
Q2
20
Q3
20
TOTAL
60
Qi]... [20 points] Consider the series
Z~
(i) Show that the series converges.
(ii) Determine an upper bound for the error made in approximating the sum of the series with the
i~artia1 sum.
ci)
10th
Lkcgn~ ~t:
S
_N6+s
I
—x
C
60
—~
tN~
L
__
L
OVER
“C
I S~c~
1
~t
S
r
b~ \~t~r4
=
H
__
Q2].
(x—1~
[20 points] Find the convergence set of the power series ~ ~ + 2
Carefully justify any
claim you make.
cd0s~~c ~*o
1$
z
r~
v~3
—~
c~UNvu~~r
-~
~
{-crf
H
~\1
t~f
I
L
~
co
x~
en
0
0
~Ez~t
1
-t
—
__
~
21)
Q3]. [20 points] Find the Taylor series of f(x)
notation.
.
.
=
%/~ around a
=
1. Write your answer in summation
±
~1
v~1~
4 C
2
-
—
Z
~o.
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