Math 22, Spring 2015, Final Exam
(1) FindZthe indicated integrals: Show the steps involved. (10 points/part)
(a)
x ln x dx
Z
(b)
cos2 (x) sin2 (x)dx
Z0
2x + 1
(c)
dx
(x + 2)(x2 + 1)
(2) Find the volume of the solid obtained by rotating the region bounded
MATH 22, SPRING, 2016, PRACTICE FINAL EXAM
Instructions. This list of problems is intended to help you prepare for the final exam. However, keep
in mind that the syllabus for the exam is all the material in the listed sections, and if a particular type
of
Name: Math 22 Quiz 6 3/22/16
1.) Find the solution to the differential equation that satises the initial condition:
_ 2t+sec2t
dt _ 2g
89., Jy : g(at+5\t)lt
; y(0) = -5-
: tVta-d-tnnti-QS
sine: we Wt 7(0): A not 7M: 7 w "4 15
113.14% rest. so, '
y = - J
Name: Math 22 Quiz 5 3/8/16
1.) Find the centroid of the region bounded by the curve y = 1 - :02 and the xaxis. (Hint: you
can use symmetry to nd one of the components of the centroid.)
49.05.17 : e
-L L
Name: Math 22 Quiz 8 4/5/16
either nd the limit if
1.) Determine if the following sequences converge or diverge. For each,
quence does converge, or explain Why it diverges.
these
n5+3n3+9n+7 n+1
='_ =
Ji'Jlbrgi) a" 4n5+6n4+n2+9 (b') b" ta(3112+n) L
M: I
Math 22 review problems for exam #1
1. The area. between y = 4.1: and y = m3 , a: Z 0, is rotated about the x
axis. Find the volume using A) shells B) washers.
2. Repeat 1A and 1B when rotated about the y axis. Distinguish correctly
between A and B '
3. A
Practice Work Problems
1. A 20ft chain with mass density 3lb/ft is lying on the ground. How much work is
performed in lifting the chain so that it is fully extended (and one end touches the
ground)?
2. A 1000 lb wrecking ball hangs from a 30 ft cable of d
MATH 22, SPRING, 1997, FINAL EXAM
This is the final exam given in the Spring semester, 1997. There are several dierences between this exam
and the exam you will have for the current course. In particular, mixing problems, centers of mass, and
conic sectio
an =
an
n
1, n
1
|1
0
lim
n!1
n
1
X
1 n
2 + 3n
n=1
x<3
x=
x
1
X
n=1
2
an (x) =
1
1) = 2 x
2
2
an (3) =
n 1
2+3n
n
n
.
1 2
2 5
|an+1 (x)|
= x
|an (x)|
x
x<
2
(2x 1)n
p
5n n
1 2
.
2 5
1 2
<1
2 5
x
1
2
<
5
2
2<
x>3
R=
x=3
x=
an (3)
|an | =
n 1
1
= < 1.
2 +
Math 2433 Homework #7 and #8
Solutions
Section 12.9.
Find the power series representation of the functions below and find the interval of
convergence of the series.
8. f (x) =
!
x
4x+1 .
Solution: We have
x
=x
4x + 1
The power series representation of
$
1
Math 22 review problems for exam #1
1. The area between y = 4x and y = x3 , x
axis. Find the volume using A) shells B) washers.
0; is rotated about the x
2. Repeat 1A and 1B when rotated about the y axis. Distinguish correctly
between A and B
3. A 50 feet
SCM Exam 3 Study Guide
(Chapters 4, 12, 13, 14, 15)
35 T/F, MC
11 Quantitative Questions
Master production schedule: MPS, MRP Calculations, Gross Requirements, Net
requirements, lot size, bill of material lot structure
Time series method (forecasting) -