Let’s develop a simple method to find infinite limits and horizontal asymptotes. Here are 3 functions that appear to look almost the same, but there are.

Slides:

Advertisements

Similar presentations

1.5: Limits Involving Infinity Learning Goals: © 2009 Mark Pickering Calculate limits as Identify vertical and horizontal asymptotes.

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.

A rational function is a function of the form: where p and q are polynomials.

3.4 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.

ACT Class Openers:

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

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.

APPLICATIONS OF DIFFERENTIATION 4. A polynomial behaves near infinity as its term of highest degree. The polynomial behaves like the polynomial Near infinity.

Limits at Infinity Explore the End Behavior of a function.

9.3 Rational Functions and Their Graphs Rational Function – A function that is written as, where P(x) and Q(x) are polynomial functions. The domain of.

Many times we are concerned with the “end behavior” of a function. That is, what does a function do as x approaches infinity. This becomes very important.

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

Limits at Infinity Horizontal Asymptotes Calculus 3.5.

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:

AP Calculus AB Chapter 3, Section 5 Limits at Infinitiy

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.

2.7 Limits involving infinity Wed Sept 16

Quadratic Functions (3.1). Identifying the vertex (e2, p243) Complete the square.

Class Work Find the real zeros by factoring. P(x) = x4 – 2x3 – 8x + 16

Rational Functions and Their Graphs

§10.2 Infinite Limits and Limits at Infinity

Algebra 2 Ch.9 Notes Page 67 P Rational Functions and Their Graphs.

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.

Rational Functions A function of the form where p(x) and q(x) are polynomial functions and q(x) ≠ 0. Examples: (MCC9-12.F.IF.7d)

HOMEWORK: WB p.31 (don’t graph!) & p.34 #1-4. RATIONAL FUNCTIONS: HORIZONTAL ASYMPTOTES & INTERCEPTS.

Finding Asymptotes Rational Functions.

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.

Calculus Chapter One Sec 1.5 Infinite Limits. Sec 1.5 Up until now, we have been looking at limits where x approaches a regular, finite number. But x.

2-6 rational functions.  Lines l and m are perpendicular lines that intersect at the origin. If line l passes through the point (2,-1), then line m must.

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

LIMITS AT INFINITY Section 3.5.

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

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.

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.

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

Lesson 21 Finding holes and asymptotes Lesson 21 February 21, 2013.

limits at infinity (3.5) September 15th, 2016

Ch. 2 – Limits and Continuity

Horizontal Asymptotes

Graphing Rational Functions

Ch. 2 – Limits and Continuity

Sec 3.5 Limits at Infinity See anything?

Lesson 11.4 Limits at Infinity

AP Calculus September 13, 2016 Mrs. Agnew

Horizontal Asymptotes

3.5: ASYMPTOTES.

Objective: Section 3-7 Graphs of Rational Functions

3. Limits and infinity.

Warm-up Solve the following rational equation..

Sec 4: Limits at Infinity

MATH 1310 Section 4.4.

RATIONAL FUNCTIONS A rational function is a function of the form:

Limits at Infinity 3.5 On the agenda:

LIMITS AT INFINITY Section 3.5.

2.6 Section 2.6.

Limits at Infinity Section 3.5 AP Calc.

Asymptotes Horizontal Asymptotes Vertical Asymptotes

2.6 Rational Functions and Their Graphs

Domain of Rational Functions

Find the zeros of each function.

MATH 1310 Section 4.4.

Asymptotes, End Behavior, and Infinite Limits

Presentation transcript:

Let’s develop a simple method to find infinite limits and horizontal asymptotes. Here are 3 functions that appear to look almost the same, but there are subtle differences. Let’s explore each as x approaches ∞

Look at the degree of each polynomial The degree of the bottom, 2, is greater than the degree of the top, 1. As x grows without bound, the bottom will dominate and the limit will go to 0

Here, the degree of the top is equal to the degree of the bottom (both are 2) The limit will be the ratio of the leading coefficients (the coefficients of the terms of highest degree).

Here, the degree of the top, 3, is greater than the degree of the bottom, 2. The numerator will dominate and this limit will grow without bound to infinity.

We can quickly find the horizontal asymptotes: y = 0, same as the limit, this is the x-axis y = 3, a horizontal line No horizontal asymptote, the function grows without bound and does not approach a single value

Here is a quick quiz for you. Find the horizontal asymptotes: The degrees are the same (3) so y = 5/3 The degree of the top is greater (4 > 2) so there is no horizontal asymptote