Chapter Two Limits and Their Properties. Copyright © Houghton Mifflin Company. All rights reserved. 2 | 2 The Tangent Line Problem.

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Presentation transcript:

Chapter Two Limits and Their Properties

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 2 The Tangent Line Problem

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 3 The Area Problem

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 4 A Strategy for Finding Limits (simplified) Use direct substitution (easiest method). If direct substitution does not work try finding an equal function that can be evaluated by direct substitution. This is usually accomplished by some algebraic technique such as factoring. Use a graph or table to reinforce your conclusion.

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 5 Definition of Limit

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 6 The Squeeze Theorem

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 7 Continuity at a Point and on an Open Interval

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 8 Continuity at a Point and on an Open Interval (cont’d)

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 9 Discontinuities

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 10 Definition of Continuity on a Closed Interval

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 11 The Intermediate Value Theorem

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 12 Definition of Infinite Limits

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 13 Properties of Infinite Limits