Math 232 Quiz 2
1.
Name:_
Simplify the following, if possible:
a)
[ ] []
b)
[
2
1
1 +3 3
3
1
[1]
][ ]
2 1 3
3 1
1 1
1 1 2
2
1 2 2 1
2. Suppose that
A
and
B
are invertible. Solve the equation for
[2]
Explain/justify any steps that are not obvious.
AXC AB=0
Math 232 Quiz 6
Name:_
1. Determine if the following transformation is one-to-one and/or onto.
T
([ ]) [
x+y
x
x +2 yz
y =
2 x+ y+ z
z
3 x +2 y+ z
]
2. Determine if the two vectors u and v
are orthogonal.
[1]
3. Find the length of
[2]
[2]
u= 3 5 5 1 2 .
[
1. SHORT ANSWER each question is worth [2 marks]
a) Solve the following system of equations:
x+ 3 y =5
3 x y=5
b) Find the value(s) c
so that the following system of equation has no solution:
cx9 y =3
xcy =1
c) Evaluate the following:
[
d) The probability
1. SHORT ANSWER each question is worth [2 marks]
a) Find a and b so that
b) If
[] [ ]
a = 2
b 1
=3 is an eigenvalue for
where
A , then show that
is the basis
cfw_[ ] [ ]
0 , 2
1 1
=7 is an eigenvalue for
2
A 2 I
c) A 6 6 matrix has 3 eigenvalues. One of t
1. SHORT ANSWER
a) Solve for
x and
[
][ ] [ ]
[10]
y
1 2 x = 0
1 3 y 5
b) Evaluate.
[
T
] [
]
][
]
1 3
1 1
+2
0 2
2 5
c) Evaluate.
[
2 1 1 2 3
3 1 2
0 1
d) If det (A )=2 and det ( B )=4 , evaluate det ( B A1 )
2. Find all values of c
[4]
[
c 0 2
A= 3 0 6
Math 232 Worksheet 3
Name:_
1. The following nutritional information is given for a single serving of Rice, Broccoli, and Chicken.
Nutrient
Rice
Broccoli
Chicken
Calories
200
50
70
Protein (g)
4
5
15
Fiber (g)
1
5
0
A particular diet dictates that a dinne
Math 232 Worksheet 2
Name:_
1. Determine the number of solutions for each of the following systems of equations (you do not have to
actually solve the equations).
a) [
| ]
b) [
| ]
c) [
| ]
2. Determine the value(s) of so that the associated linear system
Math 232 Worksheet 22
Name:_
1. Find the dot product of the following pairs of vectors and determine if they are orthogonal.
and
a)
b)
and
2. Find the length of the following vector and find a unit vector in the same direction.
3. Use the dot produc
Math 232 Worksheet 23
1. Find the cross product of the following pairs of vectors in
a)
[
]
[ ]
b)
c) [
and
]
[
]
Name:_
2. Find the equation of the following planes:
a) Orthogonal to
b) Through the point
c) Through the points
(
(
and through the point
(
Math 232 Worksheet 1
Name:_
1. Solve the system of equations using augmented matrices
a)
b)
2. Construct two different augmented matrices for linear systems whose solution set is:
,
, and
.
Calculus for Business I 104
Midterm # 1
Tuesday July 28‘“, 2015
Instructor: Keira Gunn
Name: fa! (YO/13
Student Number
You have 80 minutes to complete the examination.
No cell-phones or electronic devices other than a calculator are permitted.
There are 6
Calculus for Business I 104
Midterm # 2
Tuesday August 11th, 2015
Instructor: Keira Gunn
Name:
Student Number
.
.
You have 80 minutes to complete the examination.
No cell-phones or electronic devices other than a calculator are permitted.
There are 6 page
Calculus for Business I 104
Midterm # 2
Wednesday November 25th, 2015
Instructor: Keira Gunn
Name:
Student Number
.
.
You have 60 minutes to complete the examination.
No cell-phones or electronic devices other than a calculator are permitted.
There are 6
Calculus for Business I 104
Midterm # 1
Tuesday July 28th, 2015
Instructor: Keira Gunn
Name:
Student Number
.
.
You have 80 minutes to complete the examination.
No cell-phones or electronic devices other than a calculator are permitted.
There are 6 pages;
Alexander College
Math 102 B/C: Differential Calculus with Applications to
Commerce and Social Sciences
COURSE OUTLINE: 2015 Fall Semester (TU Sept 8-Mon Dec
14, 2015; Exam: Tu Dec 15-Sat Dec 19)
Math 102B(3 Credits)
Class Contact:
Mondays
Wednesdays
Room
MATH 105
Fall 2013
Integral Calculus with Applications to
Commerce and Social Sciences
List of Textbook Exercises
The following list of exercises from the textbook by Lial, Greenwell, and Ritchey: Calculus with
Applications (10th ed.) contains problems wh
What your paper should NOT look like
Margins are ignored.
1) a;lkasdkfj
2) ;aldksfja
3) a;lsdkfj
4) dkfjie dkfj;iefj;l
5) alkjd;ie;m;dkf
Top and left margins are respected.
Problems are squeezed
together with no space
between them.
Problems are NEXT to
ea
-Homework Guidelines for Mathematics Mathematics is a language, and as such it has standards of writing which should be observed. In a
writing class, one must respect the rules of grammar and punctuation, one must write in organized
paragraphs built with
Section 5
More Applications
Keira Gunn
Math 151 Alexander College
5.1 Absolute Extrema
Closed and Bounded Intervals
Single Critical Point Theorem
5.2 Optimization
5.3 Linear Approximation
Differentials
Linear Approximation
5.4 Newtons Method
Newtons Metho
Section 4
Graphs and the Derivative
Keira Gunn
Math 151 Alexander College
4.1 Local Extrema
Intervals of Increase and Decrease
Critical Numbers
Local Extrema
First Derivative Test for Local Extrema
4.2 Concavity
The Second Derivative
Concavity of a Graph
Chapter 3
Applications of Derivatives
Keira Gunn
Math 151 Alexander College
3.1 Related Rates
Related Rates
Strategies for Solving Related Rates Problems
3.2 Exponential Growth and Decay
Differential Equations
Proportional Growth
Newtons Law of Cooling
3.
Chapter 2
Rules for Differentiation
Keira Gunn
Math 151 Alexander College
2.1 Derivatives of Polynomials and Exponentials
Notation
Constant Rule
Power Rule
Sum of Functions
Exponentials
2.2 Product Rule and Quotient Rule
Product Rule
Quotient Rule
2.3 Der
Section 1
Limits, Continuity, and Rates of Change
Keira Gunn
Math 151 Alexander College
1.1 Limits
Limits
Limit laws
Squeeze Theorem
1.2 Continuity
Piecewise Functions
Intermediate Value Theorem
1.3 Limits at Infinity
Asymptotes
1.4 Rates of Change
Averag