Two optimization examples: Problems 64 and 68 from
4.7 in Stewart
Sean Fitzpatrick
November 6, 2013
Problem 64
Problem 64 in Section 4.7 of Stewart asks the following:
The frame for a kite is to be made from six pieces of wood. The four exterior
pieces ha
Chemistry Communication Assignment
Chemical reactions are often thought of being "bad" and many people have a negative thought about chemicals.But little these people know,chemicals are used for the good
of mankind,it does a lot for our world,it makes our
CHEMISTRY
Questions: How does mercury get into water systems and how does it affect
communities that depend on fish as a water source?
Mercury is a highly toxic element with symbol (Hg) and
atomic number 80 and it is located in the periodic table
(period
Soaps and detergents are molecules selected or designed to have both polar and nonpolar
regions so that they can dissolve oily or greasy dirt from a stain, and also dissolve in water to
carry the material away.
10. (a) ClCl
nonpolar covalent
3.2
(b) +
K
3
Mohamed Abdalaziz
Ms.Gerber
SCH3U
May 31 2015
Air Bag Gas Law
Gas laws are used for many purposes in
everyday life, that helps humans in many ways,
such as inventions like airbags that gas law is
involved. Gas law in the airbags saves many
lives such as i
MCV4U d2 D.E.L.F. Assignment
Answer all questions with full solutions. Make sure your work is legible, even after you have
scanned it, and submit it as a single file. Note that derivatives must be fully simplified for full
marks.
1. Find the derivatives o
AMDEC SCH 3U Unit #4 Test (Modules 13-16)
Aids Permitted: ALCHEM Periodic Table of Elements and Ions, calculator that has no internet access
Part A: Knowledge and Understanding [30 marks]
Multiple Choice [12]
Put a capital letter in the space beside each
AMDEC SCH 3U Unit #2 Test (Modules 5-8)
Aids Permitted: ALCHEM Periodic Table of Elements and Ions, calculator
Part A: Knowledge and Understanding [30 marks]
Multiple Choice [18]
Put a capital letter in the space beside each multiple choice question that
MCV4U d2 Curve Sketching Assignment
Answer all questions with full solutions. Make sure your work is legible, even after you have
scanned it, and submit it as a single file.
For each of the following, find (if applicable):
-x and y-intercepts
-Sign chart
MCV4U d2 Vectors Assignment
Answer all questions with full solutions. Make sure your work is legible, even after you have
scanned it, and submit it as a single file.
1. State whether each quantity is a vector or scalar. Explain.
a. Speed
b. Velocity
c. We
Quiz 6 solutions
Sean Fitzpatrick
November 28, 2013
1. Section 5.4, Problem 18: Evaluate the indenite integral
sin 2x
dx.
sin x
Solution: Since sin 2x = 2 sin x cos x, we have
sin 2x
dx =
sin x
2 sin x cos x
dx =
sin x
2 cos x dx = 2 sin x + C,
where C is
Calculus 1000A
Friday, 22nd November, 2013
Quiz # 5
Name and student number: Solutions
3
[5]
6 + t2
dt.
3t3
2
You do not have to simplify any numerical expressions.
1. Evaluate the integral
Solution: The integrand is given by
6 + t2
1
= 2t3 + t1 ,
3
3t
3
Calculus 1000A
Friday, 22nd November, 2013
Quiz # 5
Name and student number: Solutions
3
[5]
4 + v2
dv.
v3
1
You do not have to simplify any numerical expressions.
1. Evaluate the integral
Solution: The integrand is
f (v) =
4 + v2
= 4v 3 + v 1 ,
3
v
and a
Some examples and additional material on inequalities,
inverses, exponential functions, and logarithms
Sean Fitzpatrick
September 15, 2013
Since we have limited time to cover Chapter 1 material in class, Ive written up a few
more examples related to the m
Quiz 3 Solutions
Sean Fitzpatrick
October 29, 2013
The questions for Quiz 3 come from Sections 3.5-4.2. You will have to answer two of the
questions below; one or both questions may be subject to some minor modication (eg. to
a number or a function).
1. S
Quiz 4 Solutions
Sean Fitzpatrick
November 17, 2013
1. Section 4.3, Problem 46: For the function f (x) =
x2 4
,
x2 + 4
(a) Find any vertical or horizontal asymptotes for the graph of f .
Solution: Since the denominator is never negative (x2 + 4 4 > 0 for
Quiz 1 Solutions
October 13, 2013
The questions for Quiz 1 come from Sections 1.5, 1.6, 2.2, 2.3, 2.5, and 2.6, as well as
Appendix D. In some cases I have modied the questions slightly.
1. Appendix D No. 88: Suppose two sides of a triangle have lengths a
Quiz 2
October 13, 2013
The questions for Quiz 2 come from Sections 2.7-3.5. For Quiz 2 you will again have to
answer two of the questions below. One of the questions will appear exactly as it is written;
the other will have some minor modication (eg. to
Lab design
Procedure
1.The physical property I will be testing out in these five solutions
(flour,icing sugar,baking soda,citiric acid and salt) is
Hardness,Conductvity and Melting point.
2 .List of materials
What you will need to test the hardness of the
Calculus 1000A
Friday, 22nd November, 2013
Quiz # 5
Name and student number: Solutions
4
[5]
2 + 3s2
ds.
s3
1
You do not have to simplify any numerical expressions.
1. Evaluate the integral
Solution: The integrand is
f (s) =
2 + 3s2
= 2s3 + 3s1 ,
3
s
and