Math 132 Test 3
New Mexico Tech
Name_
k
1. Show the sequence
is increasing and converges to 1.
k 3
2. Write the first 5 terms and determine the infinite sum of
k 0
3.
Determine whether
3
5
k
ln n
is convergent or divergent. You must give the reason fo
ERTH 203
EXAM 1, 2012
NAME: _
1. In the space below make a sketch summarizing the rock cycle. Label all major
processes.
2. What is the relationship between Bowens reaction series and the stability of minerals
at the Earths surface?
3. In order to be call
Math 132 Calculus I Exam IA Solution. 15 February 2016 John K Locke
Name_Solution_
Perform as indicated. All problems are of equal weight. If indicated show all of your work. No
calculators, or notes are permitted. This is a 50 minute exam. There are 10
EXAMPLES OF A FINDING THE DISTANCE ALONG AN ARC.
R 20 Sept 2014 Jlocke
Consider the problem in which a person or an insect is walking along a curve that
is in a plane and is a straight line so that the motion is in both the x and the y
directions. The cur
Further Examples of the Shell Method to Generate Volumes JKLocke 16 Sept.2014
Example I
Use the method of disks to obtain the volume of the solid of revolution obtained by rotating the
region bounded by f (x) = x2 and g(x) = 2x about the line y = 1.
Solut
Integration by Trigonometrical Substitution
JKLOCKER31Jan16
I Introduction
Consider the Integral below:
dx
1 x2
On examination of the Integrand of the Integral, that is:
1
f (x) =
1 x2
it is seen that the domain of the function f excludes the points x 1.
Examples Method of Disks CAGII JLocke R23March2010,
R 9 September 2014
In the method of disks (plates) you build a dierential volume element
dV = [f (x)]2dx
Use the method of disks to nd the volume of revolution for the function
f (x) = 2 + sinx
that is r
CAGII JKLOCKE R18FEB09
The area under a curve can be approximated by covering the region
of interest by n rectangles, all of the same width, but with a height
given byf (x) = h(x). h(x) is dened such that one end is on the horizontal axis, and the other e
Math 13205 Calculus II Exam IA KEY. 10 September 2014 John K Locke
Name_
Perform as indicated all problems are of equal weight. Show all of your work. No calculators, or
notes are permitted. This is a 50 minute exam. If needed you can use the back of th
Partial Fractions by Decomposition of the Fractional Integrand
Example John Locke 2 September 2015
Suppose you have an integral of the form
2
dx = 2
1 x2
1
dx
1 x2
One way to solve this is to start o with noting that
1
1
1
= 2 + 2
1 x2 1 x 1 + x
That is,
JKLImproper Integral
Evaluate the improper integral
2
1
x2 2
dx
x 2
Notice that for the integrand the domain excludes x = 2 . That is
f (x) =
x2 2
for x = 2
/
x 2
You can remove the discontinuity to make tter work easier.
x 2
f (x) =
for x = 2
/
x 2
f
Text (TAALMANKOHN) examples and problems. 28/29 August 2014, JKLocke
Page 442 problem 53. The answer in the back of the book is incorrect.
sin (x)
dx:
cos (x) + cos2 (x)
I=
I=
du
=
u(1 + u)
u = cos (x)
du = sin (x)dx
du
u
du
1+u
I = ln u ln 1 + u +
CAGII The Method of Cylindrical Shells
Examples and Problems Part 1
JLocke R30March2010, R 11 September 2014
Often when generating a volume of revolution a dicult or intractable
integral is constructed. Therefore having alternative methods available
to ge
Practice Questions for Exam 1
t 3i 6t 2 j sin tk with 0 t
Given the position function of an object r t
velocity and acceleration vectors.
1.
F
t3
<
=
ti
,
Sint
TH )=<3t2
ATT
)
2.
Math 231
4 bt
=
2t
,
2
,
find the
>
Cost ?
.
Sint

,
>
Let u 3, 2, 1 and v
Many engineering problems can be treated and solved by using complex numbers and complex
functions. We will look at complex numbers, complex functions and complex differentiation.
Part I Complex Numbers
In algebra we discovered that many equations are not