Practice! 1. For the graph shown, which of these statements is FALSE? (A) f(x) is continuous at x=2 (B) (C) (D) (E) f(x) is continuous everywhere from.

Slides:

Advertisements

Similar presentations

AP Calculus Review First Semester Differentiation to the Edges of Integration Sections , 3.9, (7.7)

Advertisements

Limits and Continuity Definition Evaluation of Limits Continuity

Chapter 2.5  Continuity at a Point: A function is called continuous at c if the following 3 conditions are met.  1) is defined 2) exists 3)  Continuity.

C hapter 3 Limits and Their Properties. Section 3.1 A Preview of Calculus.

LIMITS Continuity LIMITS In this section, we will: See that the mathematical definition of continuity corresponds closely with the meaning of the.

Warm-Up/Activator Sketch a graph you would describe as continuous.

Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.

 A continuous function has no breaks, holes, or gaps  You can trace a continuous function without lifting your pencil.

Calculus Mrs. Dougherty’s Class. drivers Start your engines.

1 Continuity at a Point and on an Open Interval. 2 In mathematics, the term continuous has much the same meaning as it has in everyday usage. Informally,

1.4 Continuity and One-Sided Limits This will test the “Limits” of your brain!

LIMITS 2. We noticed in Section 2.3 that the limit of a function as x approaches a can often be found simply by calculating the value of the function.

Section 1.4: Continuity and One-Sided Limits

AP CALCULUS PERIODIC REVIEW. 1: Limits and Continuity A function y = f(x) is continuous at x = a if: i) f(a) is defined (it exists) ii) iii) Otherwise,

Chapter 1 Limit and their Properties. Section 1.2 Finding Limits Graphically and Numerically I. Different Approaches A. Numerical Approach 1. Construct.

Sec 5: Vertical Asymptotes & the Intermediate Value Theorem

Continuity Section 2.3.

Continuity Grand Canyon, Arizona Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002.

AP Calculus BC Thursday, 03 September 2015 OBJECTIVE TSW (1) determine continuity at a point and continuity on an open interval; (2) determine one- sided.

Continuity TS: Making decisions after reflection and review.

Continuity and Discontinuity

Section 1.4 Continuity and One-sided Limits. Continuity – a function, f(x), is continuous at x = c only if the following 3 conditions are met: 1. is defined.

10/13/2015 Perkins AP Calculus AB Day 5 Section 1.4.

We noticed in Section 2.3 that the limit of a function as x approaches a can often be found simply by calculating the value of the function at a.  Functions.

Miss Battaglia AB/BC Calculus.  What does it mean to be continuous? Below are three values of x at which the graph of f is NOT continuous At all other.

Notebook Table of content Page 1 Learning Target 1 1)1-1 A Preview of Calculus 2) 1-2 Finding limits graphically and numerically 3) 1-3 Evaluating limits.

1.6 Continuity CALCULUS 9/17/14. Warm-up Warm-up (1.6 Continuity-day 2)

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.

Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.

CONTINUITY Mrs. Erickson Continuity lim f(x) = f(c) at every point c in its domain. To be continuous, lim f(x) = lim f(x) = lim f(c) x  c+x  c+ x 

2.3 Continuity.

2.4 Continuity and its Consequences and 2.8 IVT Tues Sept 15 Do Now Find the errors in the following and explain why it’s wrong:

1.4 One-Sided Limits and Continuity. Definition A function is continuous at c if the following three conditions are met 2. Limit of f(x) exists 1. f(c)

Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.

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.

1-4: Continuity and One-Sided Limits

1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

2.7: Continuity and the Intermediate Value Theorem Objectives: Define and explore properties of continuity Introduce Intermediate Value Theorem ©2002.

Section 1.4 – Continuity and One-Sided Limits

CONTINUITY. A function f(x) is continuous at a number a if: 3 REQUIREMENTS f(a) exists – a is in the domain of f exists.

Limits and Continuity Unit 1 Day 4.

Continuity and One- Sided Limits (1.4) September 26th, 2012.

AP Calc AB IVT. Introduction Intermediate Value Theorem If a function is continuous between a and b, then it takes on every value between and. Because.

Suppose you drive 200 miles, and it takes you 4 hours. Then your average speed is: If you look at your speedometer during this trip, it might read 65 mph.

Infinite Limits Unit IB Day 5. Do Now For which values of x is f(x) = (x – 3)/(x 2 – 9) undefined? Are these removable or nonremovable discontinuities?

Warm Ups. AP CALCULUS 2.4 Continuity Obj: identify the types of discontinuity.

1.4 Continuity and One-Sided Limits Main Ideas Determine continuity at a point and continuity on an open interval. Determine one-sided limits and continuity.

Calculus 1-4 Continuity and One-Sided Limits. Vocabulary Continuous: A function that is uninterrupted in the given interval None of these is continuous.

AP Calculus AB Objectives: Determine continuity at a point, determine one-sided limits, understand the Intermediate Value Theorem.

Theorems Lisa Brady Mrs. Pellissier Calculus AP 28 November 2008.

1.4 Continuity Calculus.

Limits and Continuity Definition Evaluation of Limits Continuity

Continuity and One-Sided Limits

Warm-Up: Use the graph of f (x) to find the domain and range of the function.

Ch. 2 – Limits and Continuity

Continuity and One-Sided Limits (1.4)

Ch. 2 – Limits and Continuity

The Sky is the Limit! Or is it?

AP Calculus September 6, 2016 Mrs. Agnew

2.5 Continuity In this section, we will:

Section 2.2 Objective: To understand the meaning of continuous functions. Determine whether a function is continuous or discontinuous. To identify the.

Continuity and One-Sided Limits

1.4 Continuity and One-Sided Limits (Part 2)

Warm up!…you know you love ‘em!

Intermediate Value Theorem

1.4 Continuity and One-Sided Limits This will test the “Limits”

Warm-up How are the concepts of a limit and continuity related?

Continuity and One-Sided limits

Presentation transcript:

Practice! 1. For the graph shown, which of these statements is FALSE? (A) f(x) is continuous at x=2 (B) (C) (D) (E) f(x) is continuous everywhere from 2.

AP Calculus Unit 1 Day 7 Continuity, Composition, & Intermediate Value Theorem

Three Types of Discontinuity—Be Familiar with the Vocabulary 1.Hole when factors divide out “Removable discontinuity” 2.Asymptotes when denominator = 0 “Infinite discontinuity, nonremovable” 3.Piecewise Graph or Greatest Integer Function “Jump Discontinuity, also nonremovable”

f(x) is continuous at x=c if... Official Definition Which means...

Is f(x) continuous at x = 4? Justify your answer

Is f(x) continuous at x = 3? Justify your answer

“Remove” the discontinuity in this function by rewriting the function as a piecewise function.

Intermediate Value Thm. A continuous function takes on all y values between f(a) and f(b). As Related to The Preview Video If W is between f(a) & f(b), then W = f(c) for some c in [a,b]

Graphical Illustration of the Intermediate Value Theorem a b f(b) f(a) Any W value in here will be “hit” at least once

Intermediate Value Theorem in Action Given f(x) is continuous on the interval [0,4]. What is the minimum number of times f(x) = 8? Justify. x01234 f(x)106279

Composition of functions

Composition of functions... Is f(g(x)) continuous at x = 4?

We must evaluate Therefore f(g(x)) is continuous

Find the limit of the composition