'Sided limit' diaporamas de présentation

Objectives

Objectives. Informal definition of limits Limit laws Skip formal definition of limit (epsilon, delta) Basic computational tools. Future Applications. Limits in 3 basic calculus problems : Tangent line problem: Find tangent line to curve at given point Area problem: Find area under curve

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Do now as a warm-up:

Do now as a warm-up:. Is there some number a, such that this limit exists?. If so, find the value of a and find the limit. If not, explain why not. 1.4 Continuity. f(c) exists. exists. not continuous at c. not continuous at c. not continuous at c. continuous at c.

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Sec 4: CONTINUITY & ONE-SIDED LIMITS

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Lesson 2-2

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Continuity

Continuity. 2.3. Continuity at a point. A function is continuous at any point given three things 1. The function exists 2. The limit as x approaches that point exists 3. The function = the limit at that point. Continuous from the right/left.

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2.2 Limits

2.2 Limits. Definition of Limit: Suppose that f(x) becomes arbitrarily close to the number L ( f(x) ? L ) as x approaches a ( x ? a ). Then we say that the limit of f(x) as x approaches a is L and write. Note 1: The number a may be replaced by ?. 1. Example 1:

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Lesson 2-2 part 2

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Finding Limits A Graphical & Numerical Approach

Finding Limits A Graphical & Numerical Approach. AP Calculus August 29, 2016 Mrs. Agnew. Essential Question How do you find the limit of a function graphically and numerically? Essential Vocabulary Limit One-Sided Limit. An Introduction to Limits.

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More on Limits

More on Limits. Objectives. Students will be able to Calculate a one-sided limit using a table and a calculator Calculate a limit a limit at infinity (negative infinity) Apply rules of limits. Example 1-1. For the function. find. Example 1-2. For the function. find. Example 1-3.

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Example 3 Evaluate

Example 3 Evaluate

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