Spring 2011: MATH 1220-004
Calculus II
Wed. 16th March
Midterm Examination
Name:
Dr. R. Lodh
50 minutes
Student ID:
Instructions.
1. Attempt all questions.
2. Most of the marks will be given for the work leading to a solution, not the solution itself.
3. No calculators or cheat sheets allowech
-I. Scratch paper is on I he last page. Ask the instructor if you need some more.
LQ~5tonJ
Points Your Score
Qi
20
Q2
10
Q3
10
Q4
10
TOTAL
50
Qi]... [20 points] Determine whether
f1~
converges, and if so find its vake.
~r
fli~~
~
I
—
—
—
N
ç
[z~ (L3~
-~
C~L2~t4)
so ~
Q2].
.
.
[10 pointsj Determine whether ~1
dx
converges, and if so find its value.
ç
~XL)
c
o1~
0
F
~
I
+ -3/
1
Q3].
[10 points] Define a sequence {a~} by the rule
ía1
=
1
~w
(L~
~
N
Determine whether {a~} is increasing or decreasing and then, using any theorem you may know. show that
it. is convergent.
C~41)2
<I
0 <
~
1
a
1.~t.
ft
CL
AL0
~
•
Q4].
[10 points] Define a sequence {a~} by the rule
a~=.
Show that {a~} is convergent, and find its limit.
~
~j-L
—
~
t
L
3
-t
2
ft
a