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.

Slides:

Advertisements

Similar presentations

2.2 Limits Involving Infinity

Advertisements

Chapter 3: Applications of Differentiation L3.5 Limits at Infinity.

Miss Battaglia AP Calculus AB/BC. x -∞  ∞∞ f(x) 33 33 f(x) approaches 3 x decreases without bound x increases.

Rational Functions A rational function is a function of the form where g (x) 0.

Graphing Rational Functions

Section 5.2 – Properties of Rational Functions

Rational Functions and Their Graphs. Example Find the Domain of this Function. Solution: The domain of this function is the set of all real numbers not.

2.7 – Graphs of Rational Functions. By then end of today you will learn about……. Rational Functions Transformations of the Reciprocal function Limits.

1 Find the domains of rational functions. Find the vertical and horizontal asymptotes of graphs of rational functions. 2.6 What You Should Learn.

Infinite Limits and Limits to Infinity: Horizontal and Vertical Asymptotes.

4 Copyright © Cengage Learning. All rights reserved. Applications of Differentiation.

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.

Ms. Battaglia AB/BC Calculus. Let f be the function given by 3/(x-2) A limit in which f(x) increases or decreases without bound as x approaches c is called.

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

2.2: LIMITS INVOLVING INFINITY Objectives: Students will be able to evaluate limits as Students will be able to find horizontal and vertical asymptotes.

Limits at Infinity Horizontal Asymptotes Calculus 3.5.

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

NPR1 Section 3.5 Limits at Infinity NPR2 Discuss “end behavior” of a function on an interval Discuss “end behavior” of a function on an interval Graph:

Limits Involving Infinity North Dakota Sunset. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote.

Limits at infinity (3.5) December 20th, I. limits at infinity Def. of Limit at Infinity: Let L be a real number. 1. The statement means that for.

Copyright © Cengage Learning. All rights reserved. Applications of Differentiation.

Rational Functions and Their Graphs

Rational Functions and Their Graphs. Example Find the Domain of this Function. Solution: The domain of this function is the set of all real numbers not.

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.

L IMITS AND L IMITS AT INFINITY Limit Review 1. Limits can be calculated 3 ways Numerically Graphically Analytically (direct substitution) Properties.

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.

Sec 1.5 Limits at Infinity Divide numerator and denominator by the largest power of x in the denominator. See anything? f(x) has a horizontal Asymptote.

As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if: or.

Limits Involving Infinity Section 2.2. ∞ Infinity Doesn’t represent a real number Describes the behavior of a function when the values in its domain or.

Rational Functions and Asymptotes

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

Solving for the Discontinuities of Rational Equations 16 March 2011.

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.

HWQ. Find the following limit: 2 Limits at Infinity Copyright © Cengage Learning. All rights reserved. 3.5.

Copyright © Cengage Learning. All rights reserved.

1.5 Infinite Limits Chapter 1 – Larson- revised 9/12.

Aim: How do find the limit associated with horizontal asymptote? Do Now: 1.Sketch f(x) 2.write the equation of the vertical asymptotes.

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:

Limits at Infinity: End behavior of a Function

Section 5: Limits at Infinity. Limits At Infinity Calculus

Lines that a function approaches but does NOT actually touch.

2.6. A rational function is of the form f(x) = where N(x) and D(x) are polynomials and D(x) is NOT the zero polynomial. The domain of the rational function.

Miss Battaglia AP Calculus AB/BC. x -∞  ∞∞ f(x) 33 33 f(x) approaches 3 x decreases without bound x increases.

Limits and Their Properties 1 Copyright © Cengage Learning. All rights reserved.

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

Sect.1.5 continued Infinite Limits

limits at infinity (3.5) September 15th, 2016

Rational Functions and Their Graphs

MATH 1910 Chapter 3 Section 5 Limits at Infinity.

Sec 3.5 Limits at Infinity See anything?

26 – Limits and Continuity II – Day 2 No Calculator

Graphing Polynomial Functions

3.5: ASYMPTOTES.

2.2 Limits Involving Infinity

Sec. 2.2: Limits Involving Infinity

Sec 4: Limits at Infinity

Limits involving infinity

2.2 Limits Involving Infinity

Copyright © Cengage Learning. All rights reserved.

Limits at Infinity Section 3.5 AP Calc.

Objectives Determine (finite) limits at infinity.

Asymptotes Horizontal Asymptotes Vertical Asymptotes

MATH 1910 Chapter 1 Section 5 Infinite Limits.

Copyright © Cengage Learning. All rights reserved.

Properties of Rational Functions

Properties of Rational Functions

Limits Involving Infinity

Presentation transcript:

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 limit.

Saying the limit equals infinity or negative infinity, does not mean the limit exists. In fact, it means it doesn’t exist.

Definition of Vertical Asymptote If f(x) approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line x = c is a vertical asymptote of the graph of f.

Limits at Infinity (end behavior) If f(x) approaches L as x increases or decreases without bound, we say that f has a limit at infinity. These limits at infinity are denoted by

Definition of a Horizontal Asymptote The line y = L is a horizontal asymptote of the graph of f if

Theorem 3.10 If r is a positive rational number and c is any real number, then Furthermore, if x r is defined when x < 0, then

Limits at Infinity (as x  ±  ) and Rational Functions 1.If (degree of numerator) < (degree of denominator), then limit = 0. Horizontal Asymptote: y = 0 2.If (degree of numerator) = (degree of denominator), then limit = ratio of leading coefficients. Horizontal Asymptote: y = ratio of leading coef. 3.If (degree of numerator) > (degree of denominator), then limit = +  or - . No Horizontal Asymptote