Mathematics 100 Test #1B
Name: _
Instructor: George Ballinger
Term: Fall, 2013
Section:
The Sharp EL531 calculator may be used on this test.
Mark:
You may not use LHpitals Rule when evaluating limits.
25
Show all of your work in the space provided.
The n
Math 100 Final Exam Review Questions
1. Evaluate the following limits:
x+42
x
a) lim
x 0
1
1
b) lim x + 3 3
x 0
x
c) lim
x 0
sin x
x+1
d) lim
2
x 2 + x 2
x + 2x
2. Sketch a graph which satisfies all of the following conditions:
lim f ( x ) = 0
x 3
lim f
MATH 100 Readiness Check
Calculus will likely be one of the most challenging courses you will take in your first year university program. In
order to be successful:
You must have a strong and recent algebra and trigonometry background.
You need to have a
100 Lab 0
Name: _
Section: _
Introduction to Maple
In this lab you will learn the Maple syntax for basic number operations.
1. From the Math 100 index screen, click on Introduction to Maple.
2. Read the text explaining the commands. Type and execute the c
100 Prelab
1
Algebra
l.
Complete the following questions by hand before you go to the computer lab.
$hou
!o,.r.r rrrocl( anA $rila *ka f;cr^\ ^nsu/er in *hr Sf a.cr \clou.t.
Factor the
a\ x2
b)
followins:
lx+ 6
x' 
6x2
+ Ilx
6
2. Expand by multipl
100 Prelab 2
Functions
Complete the following questions by hand before you go to
the."n:;:t;"R
t^raRK.
Uk tte
A tvSt"l
2. Find flft) tf flx) =xsin(x). (No calculators!)
3. Ifflx)
= x2
+2s+ l, find:
a)fla)
b)flr+
1)
4.
It fl*)
= x2, find f(flx) +
5.
If /(
100 Prelab 4
Differentiation
Complete the following questions by hand before you go
g,*:.gXi.t,l?li*

1. Find the following derivatives:
ut44
'axJx
b) 4 sin3r
'dt
2. Find and evaluate the following
q
derivatives'
oLrvwo'
Giv. evac) Valuef
;il;iF"a o, .".
100 Prelab 5
Curve Plotting
Complete the following questions by hand before you go to the computer lab.
1. Find the equation of the tangent line to the curve y = sin 2x + cos x at x = 0 .
2. Find the value of c guaranteed by the Mean Value Theorem for f(x
100 Prelab 6
lntegration
Complete the following questions by hand before you go to the computer lab.
1. Find the following integrals:
a)
o)
l"^
Jx
4x+2dx
P
4t+2
dt
c I ,'4t+2
dt
J;
2.IEt
F(x) =
")
*eat
as
[: *  4u+2 du. Find,:
I r14 a*
3.letflx) = si
M100 Graphing Steps
Some or all of the following questions may be asked.
a) Find the coordinates of the x and y intercepts.
b) Find the equation of the vertical and horizontal asymptotes. If there is a horizontal asymptote does
the graph touch/cross it?
c
APPENDIX D
Precalculus Review
D.1
SECTION
Real Numbers and the Real Line
Real Numbers and the Real Line Order and Inequalities
Absolute Value and Distance
Real Numbers and the Real Line
Real numbers can be represented by a coordinate system called the re
Basic Integration Rules
Dierentiation Formula
d
[C] = 0
dx
d
[kx] = k
dx
d
[kf (x)] = kf (x)
dx
d
[f (x) g(x)] = f (x) g (x)
dx
d n
[x ] = nxn1
dx
d
1
[ln x] =
dx
x
d x
[e ] = ex
dx
d kx
[e ] = kekx
dx
Integration Formula
0 dx = C
k dx = kx + C
kf (x) d
Concavity and Second Derivative Test
Denition of Concavity
Let be a dierentiable function dened on an open interval .
1. The graph of is concave upward on if is increasing on .
2. The graph of is concave downward on if is decreasing on .
Test for Concavit
Math 100
Chapter 5 and 6 Review Exercises
1.
By definition, ln(6) is the area under the curve _ from _ to _.
2.
Classify the critical number(s) of f ( x) = ln ( x 2 + 2 x + 3) using the First Derivative Test.
( sin x )( x
y=
6
3.
Use logarithmic different
Math 100
1a)
8
d)
3
cos d
2 2 sin 2
7
Chapter 4 Review Questions
3 + 4 3 x2
b)
dx
x
sin 2 x cos 2 x
e)
dx
sin 2 x
x3 + x
dx
x
c)
tan
2
( x) dx
2.
It is estimated that t months from now, the population of a certain town will be changing at
2
a rate
Mathematics 100 Test #1A
Instructor: George Ballinger
Term: Fall, 2011
Name: _
Section:
The Sharp EL531 calculator may be used on this test.
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
Mark:
25
The n
Mathematics 100 Test #2B
Name: _
Instructor: George Ballinger
Term: Winter, 2010
Mark:
25
The Sharp EL531W calculator may be used on this test.
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
The number
Mathematics 100 Test #1B
Name: _
Instructor: George Ballinger
Term: Winter, 2010
Mark:
25
The Sharp EL531W calculator may be used on this test.
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
The number
Mathematics 100 Test #1B
Name: _
Instructor: George Ballinger
Term: Fall, 2012
The Sharp EL531 calculator may be used on this test.
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
Section:
Mark:
25
The n
Mathematics 100 Test #2A
Instructor: George Ballinger
Term: Fall, 2009
Name: _
Mark:
25
The Sharp EL531W calculator may be used on this test.
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
The number of
Mathematics 100 Test #2A
Instructor: George Ballinger
Term: Fall, 2011
Name: _
Section:
The Sharp EL531 calculator may be used on this test.
Mark:
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
25
The n
Mathematics 100 Test #2B
Instructor: George Ballinger
Term: Fall, 2013
The Sharp EL531 calculator may be used on this test.
Name: _
Section:
Mark:
Show all of your work in the space provided.
The number of marks for each question is indicated in brackets
Mathematics 100 Test #2A
Name: _
Instructor: George Ballinger
Term: Fall, 2012
The Sharp EL531 calculator may be used on this test.
Show all of your work in the space provided.
The number of marks for each question is indicated in brackets.
Section:
Mark
Mathematics 100 Test #1A
Instructor: George Ballinger
Term: Fall, 2009
Name: _
Mark:
25
The Sharp EL531W calculator may be used on this test.
You may not use LHpitals Rule when evaluating limits.
Show all of your work in the space provided.
The number of
MATH 100 TEST #4. 9
NAME: S a 31:30:11:qu 5 SCORE: _ /40
This test has 6 pages. Show all of your work for full credit. The value of each
question is given in brackets.
9 I'
2x
1. a)(5) Use the Trapezoidal Rule with n = 4 to estimate 7
1
dx t0 4