CHAPTER 2.2 AND 3. SECTION 2—LIMITS INVOLVING INFINITY—DAY 1 EQ: What is the difference between evaluating a limit at infinity and a function whose limit.

Slides:

Advertisements

Similar presentations

3.3 Rules for Differentiation

Advertisements

State the domain and range of each function. 3.1 Graphs of Exponential Functions.

We will find limits algebraically

Graphing Rational Functions

MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag Example: ,000,000 Example:

To Start: 10 Points Evaluate:. CHAPTER 4: FACTORS, FRACTIONS, AND EXPONENTS Section 4-8: Exponents and Division.

Continuity Section 2.3a.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.2 Limits Involving Infinity.

3.7 Graphing Rational Functions Obj: graph rational functions with asymptotes and holes and evaluate limits of rational functions.

10.2: Infinite Limits. Infinite Limits When the limit of f(x) does not exist and f(x) goes to positive infinity or negative infinity, then we can call.

Questions over Assignment  3R- One more thing we need to do on 8, 9, & 10.

Infinite Limits Determine infinite limits from the left and from the right. Find and sketch the vertical asymptotes of the graph of a function.

AP CALCULUS AB Chapter 2: Limits and Continuity Section 2.2: Limits Involving Infinity.

2.6 – Limits involving Infinity, Asymptotes

1 What you will learn 1. How to graph a rational function based on the parent graph. 2. How to find the horizontal, vertical and slant asymptotes for a.

1.5 Infinite Limits Objectives: -Students will determine infinite limits from the left and from the right -Students will find and sketch the vertical asymptotes.

Warmup – No calculator 4) Find the average speed in ft/sec of a ball modeled by over the time period [2,6] (feet.

Unit 1 Limits. Slide Limits Limit – Assume that a function f(x) is defined for all x near c (in some open interval containing c) but not necessarily.

2.2 Limits Involving Infinity Goals: Use a table to find limits to infinity, use the sandwich theorem, use graphs to determine limits to infinity, find.

Review Limits When you see the words… This is what you think of doing…  f is continuous at x = a  Test each of the following 1.

Improper Integrals Objective: Evaluate integrals that become infinite within the interval of integration.

Chapter 2 Review Calculus. Quick Review 1.) f(2) = 0 2.) f(2) = 11/12 3.) f(2) = 0 4.) f(2) = 1/3.

3.4 Review: Limits at Infinity Horizontal Asymptotes.

AP Calculus AB Chapter 3, Section 6 A Summary of Curve Sketching

Removable Discontinuities & Vertical Asymptotes

Chapter 5-4: Dividing Polynomials St. Augustine Preparatory School October 5, 2015.

Warm Up Find the derivative of the function: f(x) = -3x Using the Fundamental Theorem of Calculus and… Using the Rules of Derivatives Then find the.

1 Limits at Infinity Section Horizontal Asymptotes The line y = L is a horizontal asymptote of the graph of f if.

Algebra Section 8 Day 1: Exponent Properties Algebra S8 Day 1 1.

CALCULUS CHAPTER 3 SECTION 6: SUMMARY OF CURVE SKETCHING.

Section 2.2a. Limits Involving Infinity We can say “the limit of f as x approaches infinity,” meaning the limit of f as x moves increasingly far to the.

1.5 Infinite Limits. Find the limit as x approaches 2 from the left and right.

Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.

Lesson 3.5 Limits at Infinity. From the graph or table, we could conclude that f(x) → 2 as x → Graph What is the end behavior of f(x)? Limit notation:

3.5 Notes analytical technique for evaluating limits of rational functions as x approaches infinity.

Dividing Polynomials/Long and Synthetic Division Section 6.3.

CHAPTER 9 SECTION 3 RATIONAL FUNCTIONS AND GRAPHS Algebra 2 Notes May 21, 2009.

Limits Involving Infinity Section 1.4. Infinite Limits A limit in which f(x) increases or decreases without bound as x approaches c is called an infinite.

Algebra Arithmetic Sequences and Series. Vocabulary Sequence – A list of numbers in a particular order Arithmetic Sequence – A sequence of numbers.

Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.

2-2 LIMITS INVOLVING INFINITY. Let’s start by considering and y = 0 is a horizontal asymptote because Def: The line y = b is a horizontal asymptote of.

Graphing Linear Equations

Section 2.6 Rational Functions Part 2

Algebra 1 Section 5.2 Write equations of lines given slope and a point

Arithmetic Sequences and Series

Calculus - Mr Santowski

Section 5.4 Limits, Continuity, and Rational Functions

AP Calculus September 13, 2016 Mrs. Agnew

Limits at Infinity; Horizontal Asymptotes

Chapter 5-1 Exponents.

INFINITE LIMITS Section 1.5.

Objective: Section 3-7 Graphs of Rational Functions

Ellipses & Hyperbolas.

Horizontal Asymptotes

Prep Book Chapter 3 - Limits of Functions

Infinite Limits Calculus 1-5.

Infinite Limits and Limits at Infinity

Limits involving infinity

Notes Over 9.3 Graphing a Rational Function (m < n)

Day 131 – Polynomial Operations

MATH 1910 Chapter 1 Section 5 Infinite Limits.

7.4 Slope Objectives: To count slope To use slope formula.

INFINITE LIMITS Section 1.5.

Graphing Horizontal and

EQ: What other functions can be made from

Parts of an Expression EE2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient).

Section 5.4 Limits, Continuity, and Rational Functions

AP Calculus Chapter 1, Section 5

Presentation transcript:

CHAPTER 2.2 AND 3

SECTION 2—LIMITS INVOLVING INFINITY—DAY 1 EQ: What is the difference between evaluating a limit at infinity and a function whose limit is infinite?

ACTIVATION

HORIZONTAL ASYMPTOTES

VERTICAL ASYMPTOTES

Remember: The limit of a sum = the sum of the limits The limit of a quotient = the quotient of the limits The limit of a constant = the constant

FIND THE HORIZONTAL ASYMPTOTES Just divide every term by the variable with the highest exponent

FIND THE VERTICAL ASYMPTOTES

HOMEWORK Page(s): 71 #1-8 all and all parts

SECTION 2—LIMITS INVOLVING INFINITY DAY 2 EQ: What is the difference between evaluating a limit at infinity and a function whose limit is infinite?

REVIEW

ACTIVATION—EVALUATE:

SKETCH THE GRAPH

TOMORROW’S CLASS WORK Page(s): & 50

SECTION 2—LIMITS INVOLVING INFINITY DAY 2 EQ: What is the difference between evaluating a limit at infinity and a function whose limit is infinite?

WE BELONG TOGETHER CARDS

SECTION 3—CONTINUITY—DAY 1 EQ: What does it mean for a function to be continuous?

CONTINUITY

WORKING WITH LIMITS

CONTINUOUS BY EXTENSION

EXAMPLE:

INTERMEDIATE VALUE THEOREM

HOMEWORK Page(s): to 16 all

SECTION 3—CONTINUITY—DAY 2 EQ: What does it mean for a function to be continuous?

DISCONTINUITY

EXAMPLES OF DISCONTINUITY

EXAMPLES

EXAMPLE:

HOMEWORK Page(s): 80 2 – 10 and 20 – 30 evens

SECTION 3—CONTINUITY—DAY 3 EQ: What does it mean for a function to be continuous?

IN CLASS ASSIGNMENT Count off by 4s Group 1: 31 and 38 Group 2: 32 and 37 Group 3: 33 and 36 Group 4: 34 and 35 Complete them in 20 minutes and be ready to present to the class (5 min max)