2.6 Limits at Infinity
Objectives
Limits at Infinity
Horizontal asymptote
Infinite Limits at Infinity
Limits at Infinity
We write
lim f (x) = L
x
to mean that the values of f (x) approach L as x becom
3.3 Derivatives of Trigonometric Functions
Objectives
Derivatives of Trigonometric Functions
The formula
sin x
=1
x0 x
can be useful for finding some trigonometric limits. We will prove
this limit in
Preliminaries: 1.5 and 1.6
Objectives
Exponential functions
Laws of exponents
The number e and natural exponential function
Inverse functions
Logarithmic functions
Inverse trigonometric functions
Expo
2.4 The Precise Definition of a Limit
The Precise Definition of a Limit
Let f be a function defined on some open interval that contains
the number a, except possibly at a itself. Then we say that the
2.2 The Limit of a Function
Objectives
Limit of a function
Onesided limits
Infinite limits
Vertical asymptote
Limit of a function
Definition
Suppose f (x) is defined when x is near the number a. Then
2.5 Continuity
Objectives
Continuous and discontinuous at a number
Continuous from right or left at a number
Continuous on an interval
Combination and composition of continuous functions
The intermedi
2.8 The Derivative as a Function
Objectives
Derivative as a function
Differentiable functions
Higher derivatives
Derivative as a function
Recall: Derivative of a function f at a fixed number a is
f (a
2.7 Derivatives and Rates of Change
Objectives
Tangents
Velocities
Derivatives
Tangents
Recall: To find the slope of the tangent line at P, we chose a
nearby point Q and evaluated the slope joining P
3.2 The Product and Quotient Rules
Objectives
The Product Rule
The Quotient Rule
The Product Rule
If f and g are both differentiable, then
d
d
d
(f (x) g (x) = f (x) [g (x)] + g (x) [f (x)]
dx
dx
dx
I
2.1 The tangent line and velocity problem
Objectives
The tangent problem
The velocity problem
The tangent line problem
The word tangent comes from the Latin word tangens, which
means touching. A tange
2.3 Calculating Limits Using The Limit Laws
Objectives
Limit Laws
Direct Substitution Property
The Squeeze Theorem
Limit Laws
Suppose that c is a constant and that lim f (x) and lim g (x) exist.
xa
xa
Quiz 2  MATH 152 Class 4  Fall 2017
Name: 5 1 7%
FIG ID:
1. Consider the function f (x) = 1n(x + 1) on the interval [0,1]. [8 marks]
(a) Show that f is a. decreasing function on the given interva
MATH 152 ( CLASS 4)
A SSIGNMENT #2
Instructions
I highly recommend that you complete this assignment a couple of days before the quiz. This will give you
plenty of time to make sure you understand the
Transformations of Trigonometric Functions
Objectives
Amplitude
Period
Phase shift
Amplitude
The amplitude of a function is onehalf the difference between the
maximum and minimum values of the functi
The Law of Sines and The Law of Cosines
Objectives
The law of sines
Ambiguous case
The law of cosines
When to use which law
The law of sines
sin
sin
sin
=
=
a
b
c
in a triangle with sides whose len
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FIC ID:
Full Name:
Quiz 1
Calculus I
Math 151
Determine whether each statement is true or false.
3X
1. Ifx>3, then I3x=3x
1
2.ir_2<
4. If
ji J_
=/:i
3.

is onetoone, then f(x)
f
=
,thenh(O,5)=2
5.
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MATH 152 ( CLASS 4)
A SSIGNMENT #5
Instructions
I highly recommend that you complete this assignment a couple of days before the quiz. This will give you
plenty of time to make sure you understand the
Addition, Subtraction, DoubleAngle, and
HalfAngle Formulas
Objectives
Addition and subtraction formula for cosine
Addition and subtraction formula for sine
Doubleangle formulas for sine and cosine
MATH 152 ( CLASS 4)
A SSIGNMENT #8
Instructions
I highly recommend that you complete this assignment a couple of days before the Midterm. This will give you
plenty of time to make sure you understand
MATH 152 ( CLASS 4)
A SSIGNMENT #4
Midterm 1: Oct. 04 (inclass)
Instructions
I highly recommend that you complete this assignment a couple of days before the midterm. This will give you
plenty of tim
MATH 152 ( CLASS 4)
A SSIGNMENT #7
Instructions
I highly recommend that you complete this assignment a couple of days before the quiz. This will give you
plenty of time to make sure you understand the
Week 6
Complex Numbers
A complex number can be dened as ordered pair [x; y] of real numbers. This
ordered pair represent a point in the complex plane.
If z1 = [x1 ; y1 ] and z2 = [x2 ; y2 ] are two co
Week 1
The Geometry and Algebra of Vectors
TwoDimensional Vectors (in R2 )
Vectors
Vectors can be represented geometrically in the Cartesian plane as a directed
line segment;
Vectors are usually writ
Week 5
Determinants
The determinant is a function  det : Mnn ! R where Mnn is the set of all n
matrices. The determinant of A 2 Mnn is written as
n
det A or jAj :
Determinants are of more theoretical
Week 7
Markov Chains
Denition 63 (Dynamical System). A dynamical system is a nite set of variables whose values change with time. The value of the variable at a point in time
is called the state of th
Week 2
Systems of Linear Equations
Denition 19. A system of linear equations is a nite set of linear equations of
the form
a11 x1 + a12 x2 +
+ a1n xn = b1
a21 x1 + a22 x2 +
+ a2n xn = b2
.
.
am1 x1 +