today in calculus!… note-taking tips learning targets : you will represent, classify, and order...
TRANSCRIPT
TODAY IN CALCULUS!…
Note-Taking Tips
Learning Targets : You will represent, classify, and order real
numbers. You will use inequalities to represent sets of real
numbers. You will solve inequalities You will use inequalities to model and solve real-
life problems. Independent practice
NOTE-TAKING TIPS:
• NEATNESS COUNTS!!!
• Start new lessons on new pages.
• Always have a date and headings BIG ANG BOLD to be easy to find.
• You do not have to copy EVERYTHING! But should have example problems to refer to when doing assignments.
• If you do happen to miss something, lessons will be found on the class website.
0.1 INTEGERS AND RATIONAL NUMBERS:
REAL NUMBERS
RATIONAL NUMBERS
INTEGERS
WHOLE NUMBERS
…−√2,−1 ,− 12,0 ,1 ,
34,√3 ,𝜋…
…−1 ,−12,0 ,34,1 ,2 ,…
…−3 ,−2 ,−1 ,0 ,1 ,2 ,3 ,…
0 ,1 ,2 ,3 ,4 ,5…
Incl
udes
pos
itive
and
ne
gativ
e w
hole
nu
mbe
rs
Incl
udes
num
bers
that
can
be
writt
en
as a
frac
tion
IRRATIONAL NUMBERS
Includes numbers that cannot be written as a fraction
All rational and irrational numbers
IMAGINARY NUMBERSA real number multiplied by the term , where
…√−2,5 𝑖 , 𝑖3 ,…
EXAMPLE: Determine whether the real number is rational or irrational.
1. 2.
3. 4.
5.
IRRATIONAL
RATIONAL IRRATIONAL
RATIONAL
RATIONAL
PRACTICE: Determine whether the real number is rational or irrational.
1. 2.
3. 4.
5.
RATIONAL
RATIONAL RATIONAL
IRRATIONAL
IRRATIONAL
OPEN INTERVAL:
CLOSED INTERVAL:
INTERVALS NEITHER OPEN OR CLOSED:
INFINITE INTERVALS:
0.1 ORDER AND INTERVALS ON THE REAL NUMBER LINE(𝒂 ,𝒃)
𝒂 𝒃𝒂<𝒙<𝒃
[𝒂 ,𝒃]
𝒂 𝒃
𝒂≤ 𝒙≤𝒃
¿𝒂 𝒃𝒂<𝒙 ≤𝒃¿
𝒂 𝒃𝒂≤ 𝒙<𝒃
(−∞ ,𝒂)𝒂 𝒃𝒙<𝒂(𝒃 ,∞)𝒂 𝒃𝒙>𝒃
¿𝒂 𝒃𝒙≤ 𝒂
¿𝒂 𝒃𝒙≥𝒃
−∞<𝒙<∞ 𝒂 𝒃 (−∞ ,∞)
0.1 SOLVING A LINEAR INEQUALITYEXAMPLE 1: Solve the inequality and sketch the graph of the solution on the real number line.
1. 2.
Interval notation:( , ) – open intervals[ , ] – closed intervals
¿ ,>¿≤ ,≥
0.1 SOLVING A LINEAR INEQUALITYPRACTICE 1: Solve the inequality and sketch the graph of the solution on the real number line.
1. 2.
5 ∙ ∙5
0.1 SOLVING A LINEAR INEQUALITYEXAMPLE 2: Solve the inequality and sketch the graph of the solution on the real number line.
1. 2.
Multiplying or dividing by a negative number = flip inequalities!
0.1 SOLVING A LINEAR INEQUALITYPRACTICE 2: Solve the inequality and sketch the graph of the solution on the real number line.
1. 2.
Multiplying or dividing by a negative number = flip inequalities!
0.1 SOLVING A POLYNOMIAL INEQUALITY
EXAMPLE 1: Solve the inequality and give the solution in interval notation
Bring all the terms to one side
Factor the polynomial Calculate the zeros
Draw a number line and test theintervals between the zerosto find where the polynomial will be negative
Define the solution set using intervalnotation
𝟑−𝟐 𝟒𝟎−𝟑+¿ +¿−
0.1 SOLVING A POLYNOMIAL INEQUALITY
EXAMPLE 2: Solve the inequality and give the solution in interval notation
Bring all the terms to one side Combine like terms Factor the polynomial Calculate the zeros
Draw a number line and test theintervals between the zerosto find where the polynomial will be negative
Define the solution set using intervalnotation
𝟒𝟏𝟐
𝟓𝟏𝟎+¿ +¿−
0.1 SOLVING A POLYNOMIAL INEQUALITY
EXAMPLE 3: Solve the inequality and give the solution in interval notation
Bring all the terms to one side
Factor the polynomial Calculate the zeros
Draw a number line and test theintervals between the zerosto find where the polynomial will be positive
Define the solution set using intervalnotation
𝟓−𝟐 𝟔𝟎−𝟑+¿ +¿−
0.1 SOLVING A POLYNOMIAL INEQUALITY
PRACTICE: Solve the inequality and give the solution in interval notation
Bring all the terms to one side Factor the polynomial Calculate the zeros
Draw a number line and test theintervals between the zerosto find where the polynomial will be positive
Define the solution set using intervalnotation
𝟒𝟐𝟓𝟑𝟏
+¿ +¿−
0.1 WORD PROBLEMS: PRODUCTION LEVELSEXAMPLES: Use inequality notation to describe the subset of real numbers.1. The estimated daily oil
production p at a refinery is greater than 2 million barrels but less than 2.4 million barrels.
2. The revenue for selling x units of a product is , and the cost of producing x units is . To obtain a profit, the revenue must be greater than the cost. For what values of x will this product make a return profit?
𝟐𝒎𝒊𝒍𝒍𝒊𝒐𝒏<𝒑<𝟐 .𝟒𝒎𝒊𝒍𝒍𝒊𝒐𝒏
Cannot have PART of a unit…
HOMEWORK #1:
Pg.7: 5-35 odd
HEADING ASSIGNMENTS (for your benefit and mine):
• NEATNESS COUNTS!!!
• Head assignments on the upper right hand corner of the paper:Mrs. Un Per.1Date __/__/___HW#1: Pg.75-35odd