MATH M119
Exam 1
Spring 2012
Part 1
Please choose the best answer for each of the following multiple choice problems. Please record your
answers on the cover sheet.
1. Find the average rate of change of f(x) = 2x 3 + 5x 7 on the interval x= 1 to x = 3.
a.

5.1-5.3: Definite integrals and
approximations
Definite overlap with
previous material
5.1 Accumulated change
5.2 Definite integral
Recall
Velocity = rate of change of distance
In math-speak,
v(t) = D(t)
Reverse?
So, if we do the anti-derivative of veloci

Exam 3 Review
Chapters 4 and 7
Exam 3 is Tuesday, April 16
2:30-3:45 pm, in Rawles 100.
Seats will be assigned.
Please bring your Indiana University ID and a
pencil.
Exam 3 Tuesday
Please bring your Indiana University ID and a
pencil.
You may use a non-gr

2.1 Instantaneous rate of change
Derivative at a point
Recall: Average rate of change
The average rate of change, A, of a function f(x)
between x = c and x = d is given by the
familiar equation:
f ( d ) f (c )
A
d c
this is still the same as the slope equ

1.6 Logarithmic equations
left unfinished last time
Remember: Facts about logarithms
log(A*B) = log A + log B
ln(A*B) = ln A + ln B
log(A/B) = log A log B
ln(A/B) = ln A ln B
log(Bs) = s log B
ln(Bs) = s ln B
log(10s) = s
ln(es) = s
10log(u) = u
eln(u) =

Announcements
Final exam will be Tuesday, April 30,
from 12:30-2:30 pm.
Our class will be in BH 013, the same
room as we had for the midterm.
Be sure to bring Indiana University ID,
a (graphing) calculator and a pencil.
Practice Exams
There are multiple p

Announcements
Quiz 1 will be at the end of class.
No calculators may be used for this quiz.
Also, you may not use your notes, books,
computers, iPods, cell phones, or nail clippers.
You may use a pencil or pen, but please do not
use red or pink ink.
Annou

Optimization
A few geometric examples
General principles
For any optimization problem, you will:
a. Find an equation for what you are trying to
optimize, say P(x). This is called the objective
function.
General principles
For any optimization problem, you

MATH M119
Brief Survey of Calculus
Instructor information
Instructor:
Email
Jim Hendrickson
jamhendr@indiana.edu
Office: RH 227
Hours: To Be Announced
Grades
Determined by the following formula:
Assignment
Weight
Homework
10%
Quizzes
8%
Exam One
15%
Midte

Announcements
Quiz 1 on Tuesday will cover sections 1.1-1.3.
Note that calculators are not allowed on all the
quizzes before the first exam AND that
calculators will not be allowed on the first
exam (on February 5) .
This information is on the section Syl

Announcements
Quiz 2 will be at the end of class.
No calculators may be used for this quiz.
Also, you may not use your notes, books,
computers, iPods, cell phones, or other
electronic devices.
You may use a pencil or pen, but please do not
use red or pink

Midterm Exam Saturday
Starts at 9:00 am in SW 119 and SW 007.
Assigned seats.
Expect to be there 15 minutes early.
Bring pencil, ID and calculator.
Brief Review
Starting with Chapter 3
Derivative rules
Rule
Power rule
n
n 1
(x ) = n x
(k x )
n
= kn x
Exam

Optimization,
Implicit Differentiation,
and Related Rates
Oh, the places youll go!
Optimization
Geometry and Business
Examples
General principles
For any optimization problem, you will:
a. Find an equation for what you are trying
to optimize, say P(x). Th

Announcements
Exam Three will be on Thursday, April 11, during
class.
There will be a quiz today, Tuesday, April 9, at
the end of class, but no quiz on April 16.
Please make a note of this!
Announcements
Exam 3 is Thursday from 2:30-3:45 pm in RH
100.
The

4.7 Logistic Growth
Another application of concavity
New Day, New Function
Suppose we are given a function defined for t 0
L
f (t )
kt
1 Ce
where L, C, and k are all positive constants to
be named later.
New Day, New Function
Suppose we are given a
func

Announcement
We will discuss Chapter 7 before Chapters 5 and
6.
Announcement
Next week, the quiz will be on THURSDAY (3/28)
instead of the Tuesday (3/26).
Section 7.2 is difficult, so we will need the whole
75 minutes to discuss it.
7.1 Antiderivatives
An

MATH M119
Spring 2011
Exam 1
Please do each of the following in the space provided. Where there is more than one step to a
problem, you MUST show your work to receive full credit.
1. A power function is a function that can be written in the form
y k x
p
.

Announcements
Exam 1 will be held Tuesday, February 5, from
2:30-3:45 pm in RH 100.
Whats on it?
All the topics covered in lecture, Webwork,
and quizzes up to that point.
1.9 Power functions,
polynomials and
proportionality
Retro Algebra
If n is a whole n

Announcements
The 1st Exam is one week from today.
February 5, 2012, from 2:30-3:45 pm in RH 100.
Seats will be assigned.
Announcements
The quiz will be at the beginning of the hour
today.
There will be a lecture after the quiz.
Limits
End behavior of pol

2.3 Interpretations of the
1st and 2nd derivatives
Approximations
Graphs and the
1st and 2nd derivatives
Recall: 1 Derivative
st
The derivative f(a) can be thought of as:
the slope of the function at x = a
the slope of the tangent line to f(x) at x = a
th

7.3 Definite integrals
Bringing numbers back
Yeah!
Them other digits dont
know how to act!
Recall: Basic rules of integration
n 1
x
n
x dx n 1 C
4
13
x
3
13
x
dx 4 C
Recall: Basic rules of integration
n 1
x
n
x dx n 1 C
x
1
dx ln x C
4
13
x
3
13
x
dx 4

Announcements
Exam One will be Tuesday, during class, in RH
100.
Please bring your university ID and a pencil.
Seats will be assigned.
Exam 1 info
Exam 1 has approximately 18 questions:
Some problems will require correct work
shown to receive credit
The r

3.1-3.2 Derivative formulas
Part I, Day 2
Polynomials,
Power functions,
Exponentials and Logs
Notation
The first derivative of f can be denoted in two
ways
df
dx
or
f
Notation
The second derivative of f can be denoted in two
ways
2
d f
dx 2
or
f
Adding fu

2.5 Profit, Cost, Revenue
Breakeven and Approximations
(a bit more than last time)
Breakeven
The breakeven point is the quantity produced
and sold which makes profit equal to zero.
Breakeven
(alt definition)
The breakeven point is the quantity produced
an

Midterm Exam Saturday
Starts at 9:00 am in BH 013.
Assigned seats.
Expect to be there 15 minutes early.
Bring pencil, ID and calculator.
Brief Review
Starting with Chapter 3
Derivative rules
Rule
Examples
Power rule
x
n
n x
k x
n
kn x
x
n 1
5
n 1
5 x

Announcements
Midterm exam is Saturday, March 2, 2013,
from 9:00-10:30 am.
Our section will be in BH 013.
You will be allowed to use a calculator such as a
TI-84 on the midterm exam.
Midterm will cover Chapters 1, 2, and 3.
Midterm Exam next Saturday
No n

Chapter 4
Using the derivative
4.1 Local maxima and minima
4.2 Points of Inflection
4.3 Global max and min
Recall: First Derivative
The first derivative can be thought of as
the slope of the function at x = a
And we can write the first derivative as
f or

7.2 Integration with substitution
This is like a puzzle.
Recall definitions
An antiderivative of f(x) is any function F(x) with
the property that F(x) = f(x).
The indefinite integral of f(x) is the generalized
antiderivative.
Example
Find the indefinite i

Midterm Exam Saturday
Starts at 9:00 am in BH 013.
Assigned seats.
Expect to be there 15 minutes early.
Bring pencil, ID and calculator.
Brief Review
Starting with Chapter 2
Fall 07
3) A supply curve is given by S(p) = 5p 200,
while the associated demand