MAT 295 Calculus I
Final Examination
Spring 2009
Print your name
Signature
SU ID number
Print your instructor's name
Instructions. This examination has 10 problems and
10 pages (including this one).
Make sure your examination is complete before you begin
[EVENT INTRO]
[EVENT TITLE]
[EVENT SUBTITLE]
[TIME]
[LOCATION]
[ADDRESS, CITY, ST ZIP CODE]
[To replace any placeholder text (such as this), just click it and
start typing.
We think this beautiful flyer makes a great statement just as it
is. But if youd l
5.3 -Evaluating Definite Integrals
November 26, 2012
Math 295-100 ()
5.3
11/26/2012
1 / 20
Before Thanksgiving: The definite integral
If f is a function defined on [a, b] the definite integral of f from a to b is
the number
Z b
n
X
f (x)dx = lim
f (xi )xi
5.1 - Areas and distances
November 9, 2012
Math 295-100 ()
5.1
11/9/2012
1 / 22
The area problem
Find the area of the region S that lies under the curve y = f (x) between
x = a and x = b.
Math 295-100 ()
5.1
11/9/2012
2 / 22
Example
What is the area under
5.3 - Evaluating Definite Integrals
November 28, 2012
Math 295-100
5.3
11/28/2012
1 / 22
The evaluation theorem
If f is continuous on the interval [a, b], then
Z
b
f (x)dx = F (b) F (a)
a
where F is an antiderivative of f , F 0 = f .
The area under the gr
2.6 - Implicit Differentiation
October 1, 2012
Math 295-100
2.6 -Implicit Differentiation
10/1/2012
1/7
Example
Find the equation of the tangent line to the circle x 2 + y 2 = 25 at the
point (3, 4).
Solve for y :
y = 25 x 2 = (25 x 2 )1/2
The derivative
5.4 - The Fundamental Theorem of Calculus
November 30, 2012
Math 295-100 ()
5.4
11/30/2012
1 / 22
Announcements:
Final Exam:
Wednesday December 12, 10:15-12:15, Grant Auditorium (Law
School building). Final Exam is cumulative, more information on
what wil
3.2/3.3 - Logarithms
October 10, 2012
Math 295-100
3.2/3.3 -Logarithms
10/10/2012
1/1
Last time: Exponential Functions and the number e.
An exponential function is a function of the form f (x) = ax , where a is a
positive constant. For an exponential func
3.1 -Exponential Functions
October 8, 2012
Math 295-100
3.1 -Exponential Functions
10/8/2012
1 / 16
Exponential Functions
An exponential function is a function of the form
f (x) = ax
where a is a positive constant. We define ax as follows.
When x = n is a
3.5 - Inverse trigonometric functions
October 17, 2012
Math 295-100 ()
3.5 - Inverse trigonometric functions
10/17/2012
1 / 15
Last time:
Function
Domain
sin1 (x)
1 x 1
cos1 (x)
1 x 1
tan1 (x)
< x <
Math 295-100 ()
Range
2 y
Derivative
2
0y
2 y
3.5
4.1 - Maximum and Minimum values
October 24, 2012
Math 295-100 ()
4.1 - Maximum and Minimum values
10/24/2012
1 / 23
Extreme Value Theorem
If f is a continuous function defined on a closed and bounded interval
[a, b], then f has an absolute maximum and an
5.2 - The Definite Integral
November 12, 2012
Math 295-100 ()
5.2
11/12/2012
1 / 15
The definite integral
Let f (x) be a function defined on an interval [a, b]. The definite integral
of f over the interval [a, b] is written
Z b
f (x)dx
a
and is the signed
5.2 - The Definite Integral
November 14, 2012
Math 295-100
5.2
11/12/2012
1/1
Last time: The definite integral
If f is a function defined on [a, b] the definite integral of f from a to b is
the number
Z b
n
X
f (x)dx = lim
f (xi )xi
a
xi 0
i=1
where the l
4.7 - Antiderivatives
November 7, 2012
Math 295-100 ()
4.7
11/7/2012
1 / 12
Antiderivatives
An antiderivative of f is another function F such that F 0 (x) = f (x).
Math 295-100 ()
4.7
11/7/2012
2 / 12
Antiderivatives
An antiderivative of f is another func
[Add Key Event Info
Here!]
[Dont Be ShyTell
Them Why They
Cant Miss It!]
[One More Point
Here!]
[Add More Great
Info Here!]
[DATE]
[EVENT
TITLE HERE]
[You Have Room for
Another One Here!]
[Event Description Heading]
[To replace any tip text with your own,
E V E N T S C H E D U L E P L A N N E R T U E S DAY
T U E S DAY - 2 0 1 6 T U E S DAY 2 0 1 6 2 0 1 6 2 0 1 6
PROJECT/EVEN
T
ORGANIZER
To replace placeholder text with your own, just click it and start typing.
Want to try other colors for this planner? Ch
[Report Title]
[REPORT SUBTITLE]
Jon Jones | [Course Title] |
Get Started Right Away
When you click this placeholder text, just start typing to replace it all. But dont do
that just yet!
This placeholder includes tips to help you quickly format your repor
1.4 - Calculating limits.
August, 31st 2012
Math 295-100 ()
1.4 -Calculation Limits
8/31/2012
1/7
Last Time
1
Defined the limit of a function.
2
Computed some examples of limits that do exist.
3
Defined left and right hand limits.
lim f (x) = L if and onl
Announcements:
Final Exam:
Wednesday December 12, 10:15-12:15, Grant Auditorium (Law School
building). Final Exam is cumulative, more information to come.
Course Evaluations:
Remember to fill out the online teaching evaluations. You will receive
emails wi
Final Exam
Wednesday December 12, 10:15-12:15, Grant Auditorium (Law
School building).
Exam is cumulative. No calculators, no notes allowed.
Office hours next week (Carnegie 206C) :
I
I
Monday Dec. 10, 12-3
Tuesday Dec. 11, 11-2
Old final exams posted on
4.5 - Optimization
November 2, 2012
Math 295-100 ()
4.5
11/2/2012
1 / 14
Steps for solving optimization problems
1
Read and understand the problem: Identify the unknown, what are
the given quantites, and what are the given constraints.
Math 295-100 ()
4.5
Announcements:
Final Exam:
Wednesday December 12, 10:15-12:15, Grant Auditorium (Law School
building). Final Exam is cumulative, more information to come.
Course Evaluations:
Remember to fill out the online teaching evaluations. You will receive
emails wi
4.5 - Optimization
November 5, 2012
Math 295-100 ()
4.5
11/5/2012
1 / 12
Steps for solving optimization problems
1
Read and understand the problem: Identify the unknown, what are
the given quantites, and what are the given constraints.
2
Draw a diagram.
3
1.3 - The limit of a function.
August, 29th 2012
Math 295-100 ()
Intro/1.3-The limit of a function
8/29/2012
1/1
Average rate of change
y = 16t 2
The average velocity of the ball between t = 1 second and t = 2 seconds
is
y
y (2) y (1)
=
= 64 16 = 48 feet/
2.6 - Implicit Differentiation
October 3, 2012
Math 295-100
2.6 -Implicit Differentiation
10/3/2012
1 / 24
Example
The ideal gas law states that for an ideal gas,
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is
the univer
3.4 - Exponential Growth
October 15, 2012
Math 295-100 ()
3.4 - Exponential Growth
10/15/2012
1 / 26
The most important property of exponential functions is that the solve the
differential equation
y 0 = ky
where k is some constant, which we call the rela
2.1/2.2 - Derivatives and rates of change.
September 14, 2012
Math 295-100 ()
2.1/2.2 - Derivatives and rates of change.
9/14/2012
1 / 17
The tangent line
Let y = f (x), the tangent line of f (x) at x = a is the line thru the point
(a, f (a) with slope f
Exam 2 - practice problems
1. Find the derivative with respect to x of each function. You do not need
to simplify your answer at all after taking the derivative.
3 5
5
(b) x(x2 3x + 4)
(a)
(c)
x+2
x3
(d)
1
x3 +x2 +6x+4
5
(e) cos(x sin(x)
(f) ecos(x)
(g) l
2.5 - The Chain Rule
September 28, 2012
Math 295-100
2.5 -The chain rule.
9/28/2012
1 / 11
The Chain Rule
d
(f (g (x) = f 0 (g (x) g 0 (x)
dx
Or, if y = f (u) and u = g (x),
dy
dy du
=
dx
du dx
By combining the chain rule with the product and quotient rul
Process paragraph assignment
1. In this assignment, you are supposed to make a video (around 5-7 minutes) demonstrating the
basic steps to complete a task. The task could cover a wide range of topics. For example, you can
make a tutorial explaining how to
First Year Forum Syllabus
Fall 2016, 2:15-3:30 Wednesdays, 104 Tolley Hall
Madonna Harrington Meyer
Chair and Professor, Sociology
[email protected]
Course Objectives
The overall goal of First Year Forum is to give students a small course with a
faculty
Philosophy 251: Logic
Spring 2017 Syllabus
Instructor: James Lee
Sections: M102 MW 5:15-6:35 Hall of Languages 114
M103 MW 3:45-5:05 Science & Technology Ctr 1-019
e-mail: [email protected]
Philosophy Department Office: 541 Hall of Languages
Office Hours: M