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

Slides:

Advertisements

Similar presentations

Section 1.4.  “open interval”- an interval where the function values at the endpoints are undefined (a, b)  “closed interval”- an interval where the.

Advertisements

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

The right-hand limit of f (x), as x approaches a, equals L written: if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently.

1.5 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.

Sec 2.5: CONTINUITY. Study continuity at x = 4 Sec 2.5: CONTINUITY Study continuity at x = 2.

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.

2.1 Rates of Change and Limits Average and Instantaneous Speed –A moving body’s average speed during an interval of time is found by dividing the distance.

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!

Section 1.4: Continuity and One-Sided Limits

2.3 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.

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.

Miss Battaglia BC Calculus. Alternative limit form of the derivative: provided this limit exists. Note the limit in this alternative form requires that.

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 on Open & Closed Intervals Objective: Be able to describe where a function is continuous and classify any discontinuities as removable or non-removable.

2.3 Continuity. What you’ll learn about Continuity at a Point Continuous Functions Algebraic Combinations Composites Intermediate Value Theorem for Continuous.

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.

MAT 1234 Calculus I Section 1.8 Continuity

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

10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;

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

AP Calculus 1005 Continuity (2.3). General Idea: General Idea: ________________________________________ We already know the continuity of many 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.

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

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.

MAT 125 – Applied Calculus 2.5 – One-Sided Limits & Continuity.

Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework.

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.

SAT Prep. Continuity and One-Sided Limits Determine continuity at a point and an open interval Determine one-sided limits and continuity on a closed interval.

Continuity Chapter 2: Limits and Continuity.

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)

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

Limits and Continuity Unit 1 Day 4.

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

CALCULUS CHAPTER 1 Section 1.4: Continuity and One-Sided Limits Calculus Chapter 1 Section 4 1.

Definition: Continuous A continuous process is one that takes place gradually, without interruption or abrupt change.

Section 1.8 Continuity. CONTINUITY AT A NUMBER a.

AP Calculus Chapter 1, Section 4 Continuity and One-Sided Limits

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.

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

Chapter 2.3 Continuity. Objectives Continuity at a Point Continuous Functions Algebraic Combinations Composites Intermediate Value Theorem for Continuous.

1.4 Continuity Calculus.

Continuity Created by Mrs. King OCS Calculus Curriculum.

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

Copyright © Cengage Learning. All rights reserved.

Definition of Continuity A. Continuity at a Point – A function f is continuous at a point if 1. f(c) is defined 2. exists 3. *see examples.

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

Continuity and One-Sided Limits (1.4)

AP Calculus September 6, 2016 Mrs. Agnew

1.4 Continuity and One-Sided Limits

CONTINUITY AND ONE-SIDED LIMITS

1.4 Continuity and One-Sided Limits (Part 2)

Chapter 2 Limits and Continuity Section 2.3 Continuity.

1.4 Continuity and One-Sided Limits

Chapter 2 Limits and Continuity Section 2.3 Continuity.

Intermediate Value Theorem

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

Continuity and One-Sided limits

Limits and Continuity Section 2.3 Continuity.

Chapter 2 Limits and Continuity Section 2.3 Continuity.

Presentation transcript:

Calculus 1-4 Continuity and One-Sided Limits

Vocabulary Continuous: A function that is uninterrupted in the given interval None of these is continuous

Continuity

Vocabulary Removable Discontinuity: The function can be made continuous by defining f(c). Non-Removable Discontinuity: The function cannot be made continuous at one point.

Continuity

Continuity - Practice

Vocabulary One-Sided Limit: A limit that is not continuous, but does exist from only one direction Limit from the right: Limit from the left:

One-Sided Limits - Example

One-Sided Limits - Practice

Discussion

One-Sided Limits - Example

One-Sided Limits - Practice No

One-Sided Limits - Practice

Limits

Continuity - Example

Continuity - Practice

Limits - Example

Continuity - Properties

Continuity - Practice

Continuity Composites - Properties

Limits - Practice

Practice

Intermediate Value Theorem

Intermediate Value Theorem - Example

Exploration

Homework p ,7,9,11,15,17,25,26,40,43,57,60,79, 87ab,89,100