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Please correct your homework as efficiently as possible so that we have plenty of time to get through the lesson.

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Limits, Asymptotes, and Continuity Ex.

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Def. A horizontal asymptote of f (x) occurs at y = L if or Def. A vertical asymptote of f (x) occurs at values of x where f (x) is undefined (sort of). and are examples of graphs that have a hole.

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Ex. Find all asymptotes of, then sketch the graph.

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means that x approaches 2 from the right (larger than 2) means that x approaches 2 from the left (smaller than 2) One-Sided Limits Ex.

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Thm. The limit exists if both sides agree.

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Ex. For the function given, find: a. b. c.

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Ex. Find if

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Def. (loose) A function is continuous on an interval if the graph has no gaps, jumps, or breaks on the interval. Ex. Is continuous on [0,5]?

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Def. (tight) A function f (x) is continuous on an interval if, for all points c on the interval: i. exists ii. exists iii.

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Ex. Let Find a value of B so that f (x) is continuous at x = 0.

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The test on Chapter 1 will be on Monday. Next class we will review and Ill pass out a Sample Test so you know what types of questions I can ask.

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

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

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