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Math 5615H.
November 16, 2011.
2nd Midterm Exam.
Name (Print)
60 points are distributed between 5 problems.
You have 50 minutes (2:30 pm – 3:20 pm) to work on these problems.
No books, no notes, except for:
Appendix A. Exponential and Logarithmic Functions (3 pages).
Calculators are permitted, however, for full credit, you need to show step
bystep calculations.
This booklet consists of 7 page: the title page (this one), 5 pages (pp. 2–6)
contain 5 problems. The almost empty page 7 can also be used for solutions.
Some facts:
1.
The number
e
= lim
n
→∞
‡
1 +
1
n
·
n
=
∞
X
n
=0
1
n
!
= 2
.
71828
....
2.
y
= ln
x
for
x >
0
⇐⇒
x
=
e
y
;
1
n
+ 1
<
ln
‡
1 +
1
n
·
<
1
n
for
n
= 1
,
2
,
3
,....
3.
∞
X
n
=1
1
n
p
converges
⇐⇒
p >
1
.
4.
If

a
n
 ≤
c
n
for
n
= 1
,
2
,
3
,...
, then
∞
X
n
=1
c
n
converges
=
⇒
∞
X
n
=1
a
n
converges
.
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View Full DocumentMath 5615H.
November 16, 2011.
2nd Midterm Exam.
Page 2.
Problem 1.
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