(Tentative) Answers to Homework Problems
Picture contributed by Leah Smith
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MA 1128 Fall 2013 Practice Final
Name_
Please show your work !
Signature_
A. Simplify fully, eliminating all negative exponents:
(i)
(
)
(ii)
(
)
(
)
B. Solve the following absolute value inequalities and sketch the solutions on real number
lines:




MA 1128 Fall 2013 Practice Midterm 1
Name_
Please show your work !
Signature_
A. Evaluate:

 
 (
1.
) 
(
)
2.
3.
B. Evaluate the given arithmetic sums.
1.
2.
3.
4.
C. Simplify the given algebraic expression, eliminating all negative exponents.
(
)
MA 1128 Fall 2013 Practice Midterm 2
Name_
Please show your work !
Signature_
A. Plot the solution sets of the given systems of linear inequalities, identifying all
boundaries and corner points:
1. cfw_
2. cfw_
3. cfw_
B. Factor the given polynomials:
1.
MA 3260 Practice Test II
Name
10/9/12
Note: Test II is Thursday (10/11/12).
Quiz 07
1.
In Z12 , nd all solutions to the equation (x 3)(x + 1) = 0.
2.
In Z12 , multiply out the following products. Express all coecients with +s and only 0, 1, 2, ldots, 11
a
MA 3260 Practice Test I
Name
9/18/12
Note: Test I is Thursday (9/20/12). Test I will look a lot like this, but wont necessarily have as many of
each kind of problem.
Homework 01
1.
Consider the following set of statements, and determine if they are True o
MA 3260 Practice Final, Part II
Name
12/6/12
Note: Final is scheduled for Thursday, December 13th at 10:45am.
Test I
6.
Prove: Every multiple of 16 is a multiple of 4.
7.
Suppose we have ve integers related by the equation c = sa + tb. (You dont have to g
MA 3260 Lecture 15  Binets Formula and the Golden Ratio
Thursday, November 15, 2012.
Objectives: Derive Binets formula.
Before I derive Binets formula, let me explain a little more about how this works.
If we have a relational formula like
(1)
An = 4An1
MA 3260 Practice Final, Part I
Name
12/4/12
Note: Final is scheduled for Thursday, December 13th at 10:45am.
1.
Recall that the recurrence relation for the Fibonacci sequence is
(1)
An An1 An2 = 0.
a.
What is the characteristic equation for the Fibonacci
MA 3260 Lecture 18  Summary of Recurrence Relations (cont.) and Binomial Stu
Thursday, November 29, 2012.
Objectives: Examples of Recurrence relation solutions, Pascals triangle.
What if the characteristic equation has complex roots?
A quadratic equation
MA 3260 Lecture 17  Summary of Recurrence Relations
Tuesday, November 27, 2012.
Objectives: Prove basic facts about basic recurrence relations.
Last time, we looked at the relational formula for a sequence
(1)
An = 4An1 3An2 .
This form makes sense in ge
MA 2233 Practice Final, Part I
Name
12/6/12
1.
Evaluate the double integral
2.
Evaluate the double integral
to the left, and the line y = 4.
2
0
3
x
1
R
+ y2 dy
dx.
x2 y2 dA, where R is the region bounded by y = x2 below, the yaxis
3.
Convert the followi
MA 2233 Lecture 17  Completing the Square
Friday, October 12, 2012.
Objectives: Investigate behavior around critical points
Graphs of Quadratic Functions
A generic quadratic function in two variables looks something like this.
(1)
q (x, y) = ax2 + bxy +
MA 2233 Practice Final, Part II
Name
12/7/12
Practice Test I
2.
The following Maple program does the computation 2 + 4 + 6 + 8 (as well as output the values of i).
s:=0
for i from 1 by 1 to 4
do
i;
s:=s+2*i;
od;
How would you change the program so that it
MA 2233 Lecture 20  Practice 2nd Derivative Test
Friday, October 19, 2012.
Objectives: Continue behavior of quadratics around vertices and introduce 2nd derivative test.
Here are some examples of nding critical points and using the 2nd Derivative Test.
E
MA 2233 Lecture 19  More on quadratics and 2nd derivative test
Wednesday, October 17, 2012.
Objectives: Continue behavior of quadratics around vertices and introduce 2nd derivative test.
The Theorem
OK. Youve been completing the square on quadratic funct
MA 2233 Lecture 18  More on Quadratic Surfaces
Monday, October 15, 2012.
Objectives: Continue behavior of quadratics around vertices.
That pesky xyterm
In the examples of quadratic functions weve looked at, Ive conveniently left out the xyterm. What do
MA 2233 Lecture 16  Best Fit Linear and Quadratic Functions
Monday, October 8, 2012.
Objectives: Prepare for Second Derivative Test
Best Fit Linear Functions
Given a function z = f(x, y) and a point (x0 , y0 , f(x0 , y0 ) on the graph of this function, t
MA 1170 Practice Test I
1.
Name
Consider the function f(x) = x2 . Carefully plot at least ve points, and draw the graph.
1
MA 1170 Practice Test I
2
2.
In the graph of some function f below,
a.
estimate f(0.4) to two decimal places.
b.
estimate x, where f
MA 1170 Practice Test II
Name
1.
Use the product rule on the following. Dont simplify after taking the derivatives.
a.
f (x) = (x + 1) (x2 + x + 3).
b.
f (x) = (x2 + 7) (x3 2).
2.
Use quotient rule on the following. Dont simplify.
a.
h(x) =
b.
h(x) =
x2 +
MA 1170 Lecture 21  Integration and Area
Friday, April 1, 2011
Objectives: Examine the relationship between the integral and area.
Area functions
Last time, I introduced a new notation for the derivative,
at the picture below.
dy
.
dx
This notation has s
MA 1170 Practice Test III
1.
Name
For the function f(x) = 3x4 4x3 + 1, nd the x and ycoordinates of the critical points.
2.
For each of the following functions, nd the xcoordinate of the critical points, nd the signs of f , and
determine if each critic
MA 1170 Practice Final
Name
Final is at 10:15am on Monday, May 2nd.
1.
Consider the graph of some function f below.
f (x)
x
a.
Find limx1 f (x)
b.
Find limx1+ f (x)
c.
Find f (1).
d.
Is f continuous at x = 1?
e.
Find limx1 f (x)
f.
Find limx1+ f (x)
g.
Fi
MA 1170 Lecture 20  Integration  Antiderivatives
Wednesday, March 30, 2011
Objectives: Introduce antidierentiation, sum, constant multiple rules.
Antiderivatives
Up to now, weve been working on the dierential side of calculus. Today, we will start looki
MA 1170 Lecture 17  More on Absolute Maxs and Mins
Monday, March 21, 2011
Objectives: Determining maxs and mins over a closed interval
From last time, we saw that if we want to nd the maximum and minimum value of a function f over some
interval a x b, th
MA 1170 Lecture 18  Exponential and Log Functions
Wednesday, March 23, 2011
Objectives: Introduce exponential and log functions and their derivatives
Exponential functions
Consider the function
(1)
f(x) = 2x .
This is an example of an exponential functio
MA 1170 Lecture 19  Exponential Growth Model
Monday, March 28, 2011
Objectives: Explore application of exponential functions and population growth models.
The exponential growth model
Today, we will play with something called the exponential growth model
MA 1170 Lecture 16  Absolute Maxs and Mins
Friday, March 18, 2011
Objectives: Determining maxs and mins over a closed interval
We know that relative maximums and minimums occur at critical points. Suppose we had a problem like
the following.
Weve got 100
MA 1170 Homework 14 Answers
For each of the given functions, nd the critical points, the signs of f , and for each critical points, determine
whether it is a relative maximum, relative minimum, or a saddle.
1.
f (x) = x2 3.
f (x) = 2x, so x = 0 is the onl
MA 1170 Homework 15 Answers
For each of the given functions, nd the critical points, and use the second derivative test. Your answers
should be relative max, relative min, or dont know.
1.
f(x) = x2 3.
f (x) = 2x, so x = 0 is the only critical point. The