3. Find the volume of the solid obtained by rotating the region bounded by the curves
and y=9 about the y-axis.
10. Find the volume of the solid obtained by rotating the region bounded by the curves
x=1, and x=3 about the line y=1.
x=2 y ,
y=1/ x ,
x=0,
y

The American University In Cairo
Derivatives
The tangent of a curve at a point:
Suppose that we have a Curve C, and we wish to get the equation of the
tangent line to a curve C at a given point P = (a, f (a). Consider a point
Q = Q(x, y) which is near to

Lecture 3
(part 2)
New Functions from Old Functions
Sections 1.3
Appendix C
Important Note
The First Quiz will take Place on
the next Thursday, Feb 20th, 2014 In the
last 15 minutes of the lecture
The Materials covered are:
Sections: 1.1, 1.2 and 1.3.
App

Lecture 3
New Functions from Old Functions
Sections 1.3
Appendix C
Lecture 3 Objectives
Find algebraic expressions and domains of functions
that are combined using addition, subtraction,
multiplication, division, and composition.
Use completion of the s

Lecture 2
Essential Functions
Section 1.2 and
Appendices A and B
The dates of the Exams
The Midterms:
Midterm I: Saturday, March 22nd at 10:00-11.15 am
Midterm II: Saturday, May 3rd, 2014 at 10.00- 11:15 am
Lecture 2 Objectives
Find and graph linear func

Lecture 17
Summary of Curve Sketching
Section 3.5
Lecture 17 Objectives
Sketch the graphs of functions by first finding:
1) The Domain
2) The x- and y-Intercepts.
3) Possible Symmetries (Even and Odd).
4) Horizontal and Vertical Asymptotes.
5) Intervals o

Lecture 18
Optimization Problems
Section 3.7
Important Notes
1.
Quiz 4 will take Place on
The next Thursday May 16th.
The Materials are:
Sections: 3.1, 3.2 and 3.2.
Lecture 18 Objectives
Solve Optimization Problems, by:
Drawing pictures representing word

Lecture 15
Section 3.3
How Derivatives Affect
the Shape of a Graph
Lecture 15 Objectives
Use the sign of the first derivative to decide where
the function is increasing/decreasing.
Find local extrema (maximum/minimum) by:
1) Applying the First Derivativ

Lecture 13
Chapter 3
Section 3.1
Maximum and Minumum
Values
Lecture 13 Objectives
Use the function graph to find absolute (and local)
maxima (and minima).
Define and explain the significance of critical
numbers of functions.
Find critical numbers of fu

The American University In Cairo
Notes on Chapter 4
Maximum and minimum values:
Def. A function f (x) has an absolute maximum (or global maximum) at a
point c1 if f (c1 ) f (x) for all x Df . In such case f (c1 ) is the maximum
value of f (x).
Def. A func

1
Final Revision
=
1. Find the linearization L(x) of f (x) = cos x at a =
/2. Use it to approximate cos 89 .
solution L(x) = f (a) + (x a)f (a) = cos(/2) +
(x /2)( sin /2). Then L(x) = (x /2).
Near x = a, f (x) L(x). Then cos 89 L(89 ) =
(89 90 ) = 1 = /1

Homework 4 solutions
3.1 #29 Dierentiate the function u =
5
t + 4 t5 .
5
1
Write u = t1/5 + 4t5/2 and then u = 5 t4/5 + 4( 2 t3/2 ) = 1 t4/5 + 10t3/2 .
5
3.1 #58 Where does the normal line to the parabola y = x x2 at the point(1,0)
intersect the parabola

Nov 13, 2012
MACT 131 Midterm 2
AUC
Name: _ UID:_
Instructors Name: _ Section Time: _
Time Allowed: 75 minutes
Instructions:
Show all work to receive full credit.
Only scientific calculators are allowed. Graphing and
programmable calculators are not allow

October 16, 2012
MACT 131 Midterm 1
AUC
Name: _ UID:_
Time Allowed: 75 minutes
Instructions:
Show all work to receive full credit.
Only scientific calculators are allowed. Graphing and
programmable calculators are not allowed.
Problem Maximum Score
points

The American University in Cairo
Department of Mathematics and
Actuarial Science
MACT 131
Calculus I
Final
Date :
Wednesday, 23rd January 2013
Material Covered :
Chapter 1 , Chapter 2 , Chapter 3 & Chapter 4
Math131Dr.AbeerKamelWinter2013
Slide2
9thAssign

The American University in Cairo
Department of Mathematics and
Actuarial Science
MACT 131
Calculus I
Math131Dr.AbeerKamelWinter2013
Slide1
Instructor : Dr. Abeer Kamel
Office:
MathematicsandActuarial
ScienceDepartment,SSE
Building,FirstFloor,
Room1049
Off

The American University in Cairo
Department of Mathematics and
Actuarial Science
MACT 131
Calculus I
Math131Dr.AbeerKamelWinter2013
Slide1
Instructor : Dr. Abeer Kamel
Office:
MathematicsandActuarial
ScienceDepartment,SSE
Building,FirstFloor,
Room1049
Off

The American University in Cairo
Department of Mathematics and
Actuarial Science
MACT 131
Calculus I
Math131Dr.AbeerKamelWinter2013
Slide1
3rdAssignment
AppendixC
Numbers:18,24,34
AppendixD
Numbers:1,11,14,24,30,62,69,72
Duedate:Tuesday8thJanuary2013
Math

The American University in Cairo
Department of Mathematics and
Actuarial Science
MACT 131
Calculus I
Chapter
Derivatives
&
Rates of Change
7th Assignment
Sec 3.4: 12,16,18,23,41,43,44,47,48
Sec 3.5: 5,11,14,15,22,24,25,40,44,53,59
Sec 3.6: 5,14,15,27,35,5

Lecture 16
Limits at Infinity,
Horizontal Asymptotes
Section 3.4
Lecture 16 Objectives
Evaluate Limits of functions at both and .
Find Horizontal Asymptotes of function graphs.
What are and ?
is a quantity (not a real number)
that is larger than any re

Lecture 14
Section 3.2
The Mean Value Theorem
Lecture 14 Objectives
Decide when Rolles Theorem is applicable, and find a
number c, with f (c) = 0.
Apply Rolles Theorem to show that an equation has
at most one real root.
Decide when the Mean Value Theor

Lecture 12
Linear Approximations
and Differentials
Section 2.9
Lecture 12 Objectives
Find the linearization (linear approximation) of a
function f at a certain value x = a, and interpret it as
the tangent line at x = a.
Use the linearization of a functi

Related Rates Problems
Sec. 3.8
What are related rates?
Howfastisy(t)changing(i.e.,whatisdy/dt?)
Weknowtherateofchangeofanothervariable
x(t).
Ifwecanfindtherelationshipbetweenx(t)and
y(t),thenwecanfinddy/dtbyapplyingtheCHAIN
RULEandusingimplicitdifferenti

The American University In Cairo
REVISION ON CHAPTER 2
Problem 1. Find the following limits (if exist)
5 x2 2 x
x0
sin 3x
x + x2 + x3 39
(3) lim
x3
x2 9
x
(5) lim
x0 |x|
sin(x2 4)
(7) lim
x2
x2
1 + sin x 1 + tan x
(9) lim
x0
x
tan x sin x
(11) lim
x0
x s

CHAPTER I
PRECALCULUS REVIEW
I-Functions and their graphs
II-Trigonometry
III-Graphs of Second-degree equation
y = tan x
x2 + y 2 = 1
2
2
a
b
For Math 131
1
CONTENTS
I
1.
FUNCTIONS AND THEIR GRAPHS
Functions
i) Function definition
ii) The Vertical line te

MACT 131
Fall 2011
Homework 4
1. Evaluate the following limits, if they exist
x 1 1
x
2
x 1
lim 2
x 0 2x x 1
x 2 1
lim 2
x 1 2x x 1
1
1
lim x 3 5
x 0
x 2
x x 2 . x n n
lim
x 1
x 1
x 3 1
lim 3
x 1 x 6x 2 11x 6
a. lim
x 0
b.
c.
d.
e.
f.
x
x 3, if x 0
2. If

The American University In Cairo
HW1 in Derivatives
Problem 1. By the denition of the derivative, nd the derivative for the
following functions and determine the domain of the derivative in each case
(i) f (x) =
1
(ii) f (x) =
x
2x + 3
(iii) f (x) = cos

AMERICAN UNIVERSITY IN CAIRO
School of Sciences & Engineering
Math Department
FALL 2008
MATH-131
Instructor: Dr. Amani Elgammal
Date: Wednesday, October 15th, 2008
Question #
Question 1
Out of
/10
Question 2
/10
Question 3
/10
Question 4
/10
Bonus
/4
Tota

AMERICAN UNIVERSITY IN CAIRO
School of Sciences & Engineering
Math Department
FALL 2008
MATH-131
Instructor: Dr. Amani Elgammal
Date: Wednesday, October 15th, 2008
Question #
Question 1
Out of
/10
Question 2
/10
Question 3
/10
Question 4
/10
Bonus
/4
Tota