# MAT 1316.02, Business Math II (M/W 2:30 Class), Spring 2015

### 10. Key for Quiz 6

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## Homework Assignments

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Advice because I love you like you are my own:

You MUST be able to multiply and factor polynomials
to succeed in this class! You must also be proficient with properties of exponents.
If any of the problems on Factoring, or Simplifying give you trouble,
then you need to spend some time right away brushing up
your basic algebra skills. You can always use the sections recommended in the
text for review. Here are some websites with practice problems. You might try these
as well. Keep reviewing until you can multiply, factor and simplify the polynomials
given in the Chapter Warm-up and in the first assignment from section 9.1.

Additional Algebra Practice Material:

Adding and Subtracting Polynomials
Multiplying Binomials with the FOIL method
Multiplying Other Polynomials
Factoring a difference of two squares
Factoring Polynomials One
Factoring Polynomials Two
Factoring Polynomials Three
Factoring Polynomials Four
Factoring Polynomials by Grouping

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HW0:  Read and Study the following material to refresh the basic algebra skills
you are assumed to have as you begin this course. Try the given problems.
I will work examples of the most important ones during class on Wednesday.

On Integer Exponents and Properties
On Adding, Subtracting and Multiplying Polynomials
On Factoring Polynomials
On Simplifying Rational Expressions
On Rational Exponents and Properties

Note: All the algebra review sections above are also available in a pdf file you can download.

The filenames and urls to use to download are:

Practice Problems
Alg_Complete_Practice.pdfhttp://tutorial.math.lamar.edu/getfile.aspx?file=B,9,P

Practice Problems Solutions

Full Algebra Text for Review

Due: Start of class, Wed. 1/14
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HW1: Make sure you can do problems from the Practice Problems in the
reading assignment HW0 like these:

** Integer Exponents, Problems 1-9
* Rational Exponents, Problems 1-10
Radicals, Problems, Problems 1-14 (It is ok to learn these as we proceed through the semester)
* Polynomials, Problems Problems 1-10
** Factoring Polynomials, Problems 1-18

R&S Rational Expressions

Due: Start of class, Mon. 1/19
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HW2:  Do problems 1-8,10,11 from this link.
(If you are lost, study this link.
R&S (read and study) pgs 73-78 in our text (link 4 above).
Due: Start of class, Wed 1/21
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HW3:  Do problems 5-6 on page 79 of our text, using the Calculator Method
that is shown in the lecture notes.
Lecture Notes for Wednesday, 1/21
Due: Start of class, Mon. 1/26
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HW4:  We looked at examples from here and here.
Text, 2.1 Exercises, pgs 78-79: #'s 1 and 2
Text, 2.1 Exercises, pgs 78-79: #'s 5 and 6 using the Algebraic Method
Paul's Notes on Calculus - Limits, Problems 4, 5, and 6
Paul's Notes on Calculus - One Sided Limits, Problems 1 and 2
Do problems a-f on the handout I gave in class (here it is if you've misplaced it)
R&S (read and study) pgs 73-78 in our text (link 4 above).
Due: Start of class, Wed 1/28
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Our first quiz over HW1-HW4 will be Wednesday, 1/28
The only HW4 problems will be the finding the limit by the graph problems
Remember to bring your study sheet and calculator!
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HW5:  Do problems 1-8 on this handout. (Solutions)
If you find these problems confusing, here is a pdf file containing a summary of the lecture over this material and some examples.
Due: Start of class, Mon. 2/2
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HW6:  Do problems 2,3,4-8 in our text (Solutions)
(pages 105-106 - just find the derivative of these, ignore the rest of the instructions)
Do problems 1-12 here. Check your answers with the solutions available!
R&S pgs 97-106 in our text.
Due: Start of class, Wed 2/4
Note: The author's examples 5, 6, and 7 on pages 99-100 of our text are also excellent practice problems!
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HW7:  Do problems 7,8,9 in our text (pg 113).
Do handout 1 (here)
Do handout 2 (here)
R&S pgs 107-112 in our text.
Due: Start of class, Mon. 2/9
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HW8:  Do problems 7-11 in our text (pg 122).
Do the following problems on Schaum's Handout (here)
#'s 5.12 a,b,d; 5.13 a,b,c; 5.14 a,b,c
Lecture Notes for Monday, 2/9
Lecture Notes for Tuesday, 2/10
Due: Start of class, Wed 2/11
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Our second quiz over HW4-HW7 will be Wednesday, 2/11
There will be one page of limits by the algebra method, one problem of finding
the Instantaneous Rate of a Function by the definition (like HW5).
The rest of the problems will be finding the derivative by the shortcut rules
(like HW6 and HW7)
Remember to bring your study sheet and calculator!
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HW9:  Do problems7a,7b,7c,7d on the little handout (here ).
Answers to the little handout problems: (here ).
Do problems 3b,3c,17a,19,27 on the big handout (here ).
Answers to the big handout problems: (here ).

Due: Start of class, Wed 2/18
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HW10:  Do Text Problems 16-21, pg 128. ( solutions here )
Do problem 8 on the little handout (here ).
Answers to the little handout problems: (here ).
Do problems 5,35,37 on the big handout (here ).
Answers to the big handout problems: (here ).
Do all problems on the Marginal Analysis Handout: (here ).
Answers to the Marginal Analysis Handout: (here ).

Due: Start of class, Mon 2/23
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Our third quiz over HW8-HW10 will be Wednesday, 2/25
There will be problems on finding successive derivatives of a function -
some of these will need to be simplified and some will not.
There will be problems on using marginal analysis for cost, revenue and
profit functions like the handout problems.
Remember to bring your study sheet and calculator!
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HW11:  Do the sign-graph handout ( here  ).
(Answers ( here  ).
Due: Start of class, Wed 2/25
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HW12:  Do the critical points handout ( here  ).
(Answers ( here  ).
Due: Start of class, Mon 3/2
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HW13:  Do problems 3-6,8-11,14,15 on page 139 of our text.
solutions ( here )
Instead of following the text instructions for the problems,
just do them like our last examples in class:  find the critical
points, create the sign chart and sketch the graph showing all
"important" points (each critical point and the y-intercept).
Lecture Notes for Monday, 3/2
Due: Start of class, Wed 3/4
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HW14:  Do all the problems on this handout. ( solutions )
Due: Start of class, Mon 3/9
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HW15:  On today's asymptotes handout, do the following problems:

pg 754 #'s 5,7,9 (vertical asymptotes only - ignore the horizontal ones).

pg 754 #'s 11,13 (like the example we did in class)

If AC(x) = 30x + 450/x where x is 100s of items sold and AC is 1000s of dollars
cost, what is the minimum average cost and how many items should be sold to
achieve it? BONUS: What is the total cost at this sales level?

Text, page 149, #'s 6.15 a-e

Lecture Notes for Monday, 3/9
Due: Start of class, Mon 3/23
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Our fourth quiz over HW11-HW14 will be Wednesday, 3/11
The problems will be similar to the handout problems.
You must be able to take derivatives of a function, simplify the
derivatives, find all critical points, create and interpret a sign chart,
sketch the graph with all relative extreme values identified.
Remember to bring your study sheet and calculator!
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HW16:  Logs handout (here) Problems pg 708, #'s 1-11,19-37 odd.
Some student solutions to some of the 11.1 hw problems
Some sample problems from old quizzes (with solutions)

Lecture Notes for Monday, 3/23
Due: Start of class, Wed 3/25
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HW17:  Exponential Functions Handout (here) Problems pg 714, #'s 1-33 odd.
Some student solutions to some of the 11.2 hw problems

Lecture Notes from Wednesday, 3/25
Due: Start of class, Mon 3/30
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Our fifth quiz over HW16-HW17 will be Wednesday, 4/1
(No questions from HW15 on Asymptotes, Concavity, or Graphing)
The problems will be similar to the handout problems (HW16 & HW17) and examples worked in class.
Remember to bring your study sheet and calculator!
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HW18:  Logs handout (here) Problems pg 708, #'s 43a,b; 52.

Lecture Notes for Monday, 3/30 and some 3/25 notes
Due: Start of class, Wed 4/1
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HW19:  Do problems 7-19 odd on this handout (Implicit Differentiation).

Due: Start of class, Mon 4/6
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HW20:  Do problems 1,3,5,7,9,17,18,19,23,24,29 from this handout (Related Rates).
Missing pages from above handout

Lecture Notes from Monday, 4/6
Due: Start of class, Wed 4/8
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HW21:  Functions of Two Variables - Intro and Partial Derivatives
Some of the text examples are representative of what you need to know how
to do from these pages. They are:

pg 236, ex 4a, 4b, ex 5;
pg 258, ex 3; pg 259, ex 4, ex 5;

Do the following problems from the text:

pg 249, #'s 1a, 1b, 1e

pgs 262, #'s 1-16, 19-20
Solutions

Lecture Notes from Wednesday, 4/8
Due: Start of class, Mon 4/13
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Our sixth and last quiz over HW19-HW21 will be Wednesday, 4/15
The problems will be similar to the handout problems (HW19 - HW21), text problems, and examples worked in class.
Remember to bring your study sheet and calculator!
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Some good examples of the homework problems from 11-3 and 11-4
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HW22:  Functions of Two Variables - Optimization

Do the following problems from the text:

pg 272, #'s 1-8, ( solutions )

Lecture Notes from Monday, 4/13
Due: Start of class, Wed 4/15
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HW23:  Optimization of Two-Variable Functions

Do the following problems from the text:

pg 272, #'s 7-10

Lecture Notes from Wednesday, 4/20
Lecture Notes from Thursday, 4/21
Due: Start of class, Wed 4/22
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HW24:  Optimization of Two-Variable Functions, Antiderivative/Integrals

Do the problems on this handout.

Do the following problems from the text:  pg 196, #'s 1-10

Lecture Notes from Thursday, 4/23
Due: Start of class, Mon 4/27
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HW25:  Substitution Rule:
From this website - Do problems 1-4, and 17a,b,c

Definite Integrals:
From this website Do problems 2-9. (Solutions are on the site).

Area between curves:
Do problems 7 and 13 on page 213.

Continuous Income Streams:
Do these problems.
(solutions )

Lecture Notes from Monday, 4/27
Due: Start of class, Wed 4/29
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Some good notes and examples on basic integrals

Good extra practice problems on simple integrals with solutions
In particular, try problems 1-13 and 17-20
Excellent notes and examples on using the Substitution Rule
(Just ignore anything that has trig functions like "sin", "cos", "tan" in it)
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HW26:  Total Cost, Revenue and Profit functions from marginal functions handout.

Lecture Notes from Wednesday, 4/29
Do problems 1,3,5,7b,9a,11 from this handout.
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Final Material:

1) Be able to find the partial derivatives and use them to find critical points and
maximimums, minimums and saddle points of functions of two variables (HW 22,23,24a).

2) Be able to find basic integrals (HW 24b, the link on "Good extra practice problems on simple integrals"),
definite integrals (HW 25b), and more complicated integrals using the
substitution method (HW25a).

3) Be able to do simple area under curve problems (HW25c).

4) Be able to do continuous income stream problems (HW25d).

5) Be able to do applications on finding the total cost, revenue and profit functions from
the marginal functions (HW26).

You may bring up to 4 pages of study notes.

You may take the exam either on
Saturday, May 2nd from 3:15-5:15pm or on
Tuesday, May 5th from 1:00-3:00pm.
Both exams are in our regular classroom.

Feel free as you are studying to take a picture of your problem and email it to me
for advice. Do NOT just ask me, "How do I do problem 17" without showing my some work.
I will NOT do homework for you, but I am delighted to help any student who is giving
an honest effort!

I have enjoyed having you in my class this semester immensely!
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Note: On all emails for this course, start the subject line out with
MAT1316, followed by whatever else is appropriate. Emails without this
subject line formatting may not be accepted!

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