MATH 138 Assignment 8
Due Friday July 6
Keep an eye on the WD deadline: July 9th 2012
1. Determine if the following series converge or diverge.
(a) pg. 726 # 6:
n1
2 n
n=1 n
(b) pg. 726 # 12:
(2k 1)(k 2 1)
2
2
k=1 (k + 1)(k + 4)
1
en
(c) pg. 726 # 28:
n=1
MATH 138 Solutions 8
1. Determine if the following series converge or diverge.
(a) pg. 726 # 6:
n1
2 n
n=1 n
Solution: Try the Comparison Test.
1
The series
3
n2
n1
n
1
2 = 3
2 n
n
n n
n2
is a p-series with p > 1, so it converges. By the
Comparison Test,
MATH 138 Assignment 7
Due Friday June 29
1. Use resources from 11.2 or before. Dont use anything from 11.3 or
later.
(a) an =
5n
. Determine whether cfw_an converges, and detern=1
1 8n
mine whether
an converges.
n=1
(b) pg. 711 # 22: Determine whether th
MATH 138 Solutions 7
1. Use resources from 11.2 or before. Dont use anything from 11.3 or
later.
(a) an =
5n
. Determine whether cfw_an converges, and detern=1
1 8n
mine whether
an converges.
n=1
Solution: To see if cfw_an converges, we nd lim
n
This be
MATH 138 Assignment 6
Due Friday June 22
This assignment is meant to help you recall the information presented in
lectures 17 and 18, and to apply it.
1. Find a formula for the general term an of the sequence:
1 1 1 1
, ,
, , .
3 9 27 81
5 5 9 9 13 13
1,
MATH 138 Solutions 5
1
1. (a) pg. 527 # 38: Evaluate the integral, if it is convergent:
0
Solution: Let w =
1
1
, then dw = 2 dx
x
x
As x 0, w
As x 1, w 1
1
Therefore the integral becomes:
wew dw
=
wew dw, which we evaluate by parts.
1
Let u = w, dv = e
MATH 138 Assignment 5
Due Friday June 15
1
1. (a) pg. 527 # 38: Evaluate the integral, if it is convergent:
0
1
ex
dx
x3
(b) pg. 529 # 69: Show that a must be at least 1000 for
1
dx < 0.001.
2+1
x
a
2. (a) pg. 592 # 10: Sketch a direction eld for the dier
MATH 138 Solutions 6
This assignment is meant to help you recall the information presented in
lectures 17 and 18, and to apply it.
1. Find a formula for the general term an of the sequence:
(a) pg. 700 # 14:
Solution: an =
(b)
1,
1 1 1 1
, ,
, , .
3 9 27
MATH 138 Assignment 4
Due Friday June 1
Remember to write your name and Family Name as it appears on Quest on
the top of your rst page, and underline your Family Name. Thank you! Do
not forget to attach your Maple assignment to this one and submit both.
1
MATH 138 Solutions 3
1. (a) If
P (x)
P (x)
=
, where each linear factor
Q(x)
(a1 x + b1 ) (ak x + bk )
(ai x + bi ) is distinct, write the partial fraction decomposition for
P (x)
Q(x)
Solution:
P (x)
A1
Ak
=
+
Q(x)
a1 x + b 1
ak x + b k
(b) Do the same a
MATH 138 Solutions 4
1. pg. 438 # 12: Find the volume of the solid obtained by rotating the
region bounded by y = ex , y = 1, and x = 2 about y = 2. Sketch the
region, solid, and a typical disk/washer.
Solution: The attached sheet shows the sketch of the
MATH 138 Assignment 2 Solutions
a
1. pg. 469 # 36 (variation): Find the integral of
where a R.
es sin (a s) ds,
0
Solution: Let u = sin (a s); dv = es ds
du = cos (a s) ds; v = es . Dont forget the chain rule here.
a
0
es sin (a s) ds = [es sin (a s)]a +
MATH 138 Assignment 3
Due Friday May 25
1. (a) If
P (x)
P (x)
=
, where each linear factor
Q(x)
(a1 x + b1 ) (ak x + bk )
(ai x + bi ) is distinct, write the partial fraction decomposition for
P (x)
Q(x)
(b) Do the same as in a) for
P (x)
P (x)
=
, where
MATH 138 Assignment 2
Due Friday May 18
a
1. pg. 469 # 36 (variation): Find the integral of
where a R.
es sin (a s) ds,
0
2. Recall trigonometric integration from section 7.2.
sin3 ( x)
dx
(a) pg. 476 # 6: Evaluate the integral
x
(b) pg. 477 # 38: Evaluat
MATH 138 Assignment 1
Due Friday May 11
1. Recall FTC 1 on page 388.
r
(a) pg. 395 # 10: Find the derivative of the function g(r) =
x2 + 4 dx
0
2x
(b) pg. 395 # 58: Find the derivative of f (x) =
arctan t dt
x
2. Recall FTC 2 on page 391.
b
(a) Find
a
4
d
MATH 138 Assignment 1 Solutions
1. Recall FTC 1 on page 388.
r
(a) pg. 395 # 10: Find the derivative of the function g(r) =
0
Solution:
=
x2 + 4 dx
r
d
d
g(r) =
dr
dr
0
r2 + 4 by FTC 1.
2x
(b) pg. 395 # 58: Find the derivative of f (x) =
Solution:
=
d
dx
CO250/CM340 I NTRODUCTION TO O PTIMIZATION HW 10
Due Date: Monday, 25th July, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the as
CO250 I NTRODUCTION
TO
O PTIMIZATION - HW 11
This assignment covers material in Chapters 6 and 7. This assignment will not be graded, but you are expected
to know the material covered. Solutions are posted on UW-ACE.
Exercise 1.
Consider the following LP,
CO250/CM340 I NTRODUCTION TO O PTIMIZATION HW 3
Due Date: Friday, 27th May, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the assi
CO250/CM340 I NTRODUCTION
TO
O PTIMIZATION HW 9
Due Date: Friday July 15th, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the assi
CO250/CM340 I NTRODUCTION TO O PTIMIZATION HW 7
Due Date: MONDAY, July 4th, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the assi
CO250/CM340 I NTRODUCTION
TO
O PTIMIZATION HW 4
Due Date: Friday, June 3rd, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the assi
CO250/CM340 I NTRODUCTION TO O PTIMIZATION HW 5
Due Date: Friday, June 10th, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the ass
CO250/CM340 I NTRODUCTION TO O PTIMIZATION HW 8
Due Date: Friday, 8th July, by 2PM, in the drop box outside the Tutorial Center.
Late assignments will not be graded.
Important information: While it is acceptable to discuss the course material and the assi
Solutions from last three questions of Mini Case
4. Assuming bondholders are fully informed and they act rationally, they will
expect the stockholders to act in their best interest and not expand, so the price
of the bonds will not change.
If the expansio