Lecture Notes for Section 2.5
2.5 The Chain Rule (p. 96)
Review of decomposition:
Example 1: Decompose h into two simpler functions f and h for which h = fg:
a. h(x) = sin(x2 + 3x):
b. h(x) = (4 x2)7:
Lecture Notes for Section 2.2
1
Interpretation # 1: Instantaneous rate of change (p. 71)
Slope of tangent line/instantaneous rate of change at a:
mtan = lim
x c
f ( x ) f (c )
f (c h ) f (c )
= lim
h
Lecture Notes for Section 2.6
1
2.6 Implicit Differentiation (p. 106)
Introduction:
We know how to find the slope of a line tangent to the graph of a function.
How can I find the slope of the line tan
Lecture Notes for Section 2.3
1
Aside on exponents/radical notation:
If a1/n =
n
a
is defined, then am/n = (a1/n)m = (am)1/n:
a
n
m
n
am
Example A: Rewrite in other form:
Radical:
a.
Exponential
x3
Lecture Notes for Section 2.1
1
2.1 Instantaneous rates of change: the derivative (p. 57)
Estimating instantaneous rate of change/slope of tangent line:
For f(t) = 16t2 + 64t + 5
To estimate the slope
Lecture Notes for Section 1.5
1
1.5 Continuity (p. 37)
Idea and definition of continuity (p. 37)
Idea of being continuous over an interval: Can draw curve over interval without
.
Definition 3: Continu
Lecture Notes for Section 2.4
1
2.4 Differentiation Formulas (p. 85)
Product Rule (p. 85)
y =fg; y =
Example 1: Find the following using the product rule:
a. h(t) = (t3 + 1)
t
;
h(t) =
b. y = 3t2cost;
Lecture Notes for Section 1.2, Plus
1
Aside on distance and absolute value:
distance of a from 0: |a|
distance from a to b: |a b| = |b a|
Exercise A: Write the distances between the two specified poin
Lecture Notes for Section 1.4
1
1.4 one-sided limits (p. 30)
Example 1: Find the following using the function from Example 17 of Section 1.4 on p.
31:
x,
f ( x )
3 x,
a.
0 x 1
1 x 2
lim f(x) =
b.
x
Lecture Notes for Section 1.3
1
Aside on absolute value:
Let a be a variable:
Is a positive or negative?
Is a positive or negative?
a,
a
a,
a 0
a0
Example A: Rewrite the following without absolute
Section 1.2-Due January 31, 2011
Algebra Aerobics, p. 18: 1, 2 Exercises, p. 19-22: 9, 12, 14, 16, 18
Algebra Aerobics, p. 18 : 1a. Describe: Here we take an x, square it and multiply by 3, then subtr
Review Sheet Test 1 over Sections 1.1-2.9 Given Friday, February 18, 2011
The link for the 3rd edition (see Blackboard site) has links to web quizzes. There you can find chapter quizzes for Chapter 1
January 31, 2011
Visualizing Data
Announcement
The tutor room is open now-Mondays, Tuesdays, and Thursdays, 6-10 pm in Taylor 220.
Jesus Often Taught with Stories
We call them parables Used situatio
January 28, 2011
Now to Section 1.2 Describing Relationships between Two Variables
Ways to Visualize Two-Variable Data
Table Scatter Plots Equations (is actually one of our goals for ways to descr
MAT 1143
College Algebra Click to edit Master subtitle style Spring 2011 January 26, 2011
Section 1.1
The book titles it Describing Single Variable Data
Variable
Something that changes from person to
MAT 1143
College Algebra Click to edit Master subtitle style Spring 2011 January 24, 2011
Roll-Using I-clickers For the roll, enter letter when name appears in blue (in middle) Confirm by entering
February 16, 2011
Click to edit Master subtitle style Review for Exam
Reminder
Exam 1 will be on Friday, February 18 It will cover material from 1.1 through 2.9
Review
Important topics for upcoming
February 14, 2011
Sections 2.4 Master Click to edit & 2.9 subtitle style
Reminder
Exam 1 will be on Friday, February 18 It will cover material from 1.1 through 2.9
Slant on Data
As we see data prese
February 7, 2011
Sections 2.1-2.3 Click to edit Master subtitle style
Graphs with Stories
Obj104
Obj105
Which student is in trouble with their parents?
Why? How might they slant the truth?
Obj106
Av
Feb 4, 2011
Sections 1.4-1.5 Click to edit Master subtitle style
More Terms About Functions
Domain-set of possible inputs
May be specified Like Positive Reals Or all reals but x = 3 May be merely im
February 2, 2011
Section edit Click to 1.3 Master subtitle style
Function
What something does Romans 11:4-5
Just as our bodies have many parts and each part has a special function, so it is with Chr
February 11, 2011
Click to edit Master subtitle style Sections 2.7-2.8
Reminder
Exam 1 will be on Friday, Feb. 18 (1 week away). It will cover material from 1.1 through 2.9
Review
Important topics for
February 9, 2011
Click to edit Master subtitle style Sections 2.5 and 2.6
What if Rate of Change is Constant?
If the average rate of change is ALWAYS the same We drop the average Say rate of change
Review for Test 2 Friday, March 11, 2011 Sections 3.1-3.3, 4.1-4.3, 4.5
Create systems of equations to model linear functions and use model to compare the functions (find solution to the system) (Q2),
March 9, 2011
Click to edit Master subtitle style Review For Exam
Exam 2
Exam 2 will be Friday, March 11 It will cover 3.1-3.3, 4.1-4.3 and 4.5
Solve |x-1| = 3
A: 4 only B: 4 and -4 both C: 4 and
March 7, 2011
Click to edit Master subtitle style Sections 4.5b
Exam 2
Exam 2 will be Friday, March 11 It will cover 3.1-3.3, 4.1-4.3 and 4.5
What about am/n
Obj101
This gives meaning to ALL fract
March 4, 2011
Click to edit Master subtitle style Sections 4.5a
Exam 2
Exam 2 will be Friday, March 11 It will cover 3.1-3.3, 4.1-4.3 and 4.5
Fractional Exponents
In 4.2 we used positive integer
March 1, 2010
Click to edit Master subtitle style Sections 4.2-4.3
Exam 2
Exam 2 will be Friday, March 11 It will cover 3.1-3.3, 4.1-4.3 and 4.5
Exponents
We looked at problems like 108 to express L