'Removable discontinuity' presentation slideshows

2.1k views • 41 slides

Limits and Their Properties

1. Limits and Their Properties. 1.4. Continuity and One-Sided Limits. Continuity at a Point and on an Open Interval. Continuity at a Point and on an Open Interval.

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Hosted by Professor Nance

Jeopardy. Hosted by Professor Nance. Definitions. Grab Bag. Limits. Continuity. Graphs. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 400. 400. 400. 400. 400. 500. 500. 500. 500. 500. Final Jepardy. Row 1, Col 1.

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What is a limit ? When does a limit exist? Continuity Discontinuity Types of discontinuity

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Always, Sometimes , or Never True

Solve for x. Always, Sometimes , or Never True. Limits. Derivatives. 10. 10. 10. 10. 20. 20. 20. 20. 30. 30. 30. 30. 40. 40. 40. 40. 50. 50. 50. 50. Click here for game DIRECTIONS. Hardtke Jeopardy Template 2011. 10 Always, Sometimes, or Never.

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Continuity and One Sided Limits

Section 2.4. Continuity and One Sided Limits. Continuity. To say a function is continuous at x = c means that there is NO interruption in the graph of f at c. The graph has no holes, gaps, or jumps. Breaking Continuity. 1. The function is undefined at x = c. Breaking Continuity. 2.

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Mini Math Wars

Mini Math Wars. Review of Limits Windows vs. Doors I will pick a person to answer. If correct = +1; If incorrect ? other team can steal that point. Round is over after pts awarded; question goes to other side of room. Mini Math Wars. #1) . Mini Math Wars. #2) . Mini Math Wars. #3) .

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3.2: Continuity

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1.2 Functions & their properties

1.2 Functions & their properties. Notes 9/28 or 10/1. Relations. Every relation has a domain and range Domain : x values, independent Range: y values, dependent Functions: x value DO NOT REPEAT Examples: {(12, 4), (8, 3), (3, 9)} domain: {3, 8, 12}, range: {3, 4, 9}, is a function.

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2.3 Continuity and Intermediate Value Theorem

2.3 Continuity and Intermediate Value Theorem. Continuity. A function is continuous if you can draw the graph without picking up your pencil. Definition: A function y = f(x) is continuous at an interior point c in its domain if. (the limit has to equal the value of the function at c ).

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Definition of Limit

Definition of Limit. Lesson 2-2. Verbal Definition of Limit. L is the limit of f ( x ) as x approaches c if and only if L is the one number you can keep f ( x ) arbitrarily close to just by keeping x close to c , but not equal to c . Example: A rational algebraic function .

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Section 1.5: Infinite Limits

Section 1.5: Infinite Limits. 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. Infinite Limits. The limit statement such as

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Section 1.5: Infinite Limits

Section 1.5: Infinite Limits. 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 . . Infinite Limits.

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Integrals on the Calculator, discontinuous integrable functions

Section 5.2b. Integrals on the Calculator, discontinuous integrable functions. Do Now: Exploration 1 on page 264. It is a fact that. With this information, determine the values of the following integrals. Explain your answers (use a graph, when necessary). 1. 4. 2. 5. 3. 6.

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Limits of Functions and Continuity

Limits of Functions and Continuity. The Limit of a Function. The limit as x approaches a ( x ? a ) of f ( x ) = L means that as x gets closer and closer to a (on either side of a ), f ( x ) must approach L . Here, f ( a ) does not need to exist for the limit to exist. ?. ?.

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Continuity & IVT

Continuity & IVT. Section 1.4. Continuity at a Point. A function f is continuous at c if the following three conditions are met. f(c) is defined exists. Continuity on an open interval.

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Determining Limits From Equations

Determining Limits From Equations. The Limit Properties found on p.35 of the textbook can be used. Examples: 1) Determine . Indeterminate Limits. Example 1 : Find. Methods of Finding Indeterminate Limits. Factor and Cancel Expand and Simplify Rationalize the Denominator

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Review Questions Unit 7

Review Questions Unit 7. It takes 9 hours for John to paint a house. Jerry can paint the same house in 7 hours. How long will it take them to paint the house if they work together?

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