RULES FOR LIMITS

Nov 20, 2014

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RULES FOR LIMITS. Learning Outcomes:. Learn some rules for limits (without proof) which are required for differentiation. Rules for Limits. Differentiation. Rules for Limits. Differentiation. Rules for Limits. 12. 13. 14. 15. Differentiation.

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RULES FOR LIMITS

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RULES FOR LIMITS Learning Outcomes: • Learn some rules for limits (without proof) which are required for differentiation
Rules for Limits Differentiation
Rules for Limits Differentiation
Rules for Limits 12. 13. 14. 15. Differentiation

Limits

Limits. What is a Limit?. Limits are the spine that holds the rest of the Calculus skeleton upright. Basically, a limit is a value that tells you what height (y-value) a function is headed for or intended for, as you get close to or approach a specific x-value.

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RULES FOR

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Limits

Limits. Dr. Jane Frankenberger, Purdue University Agricultural & Biological Engineering. Four Types of Limits. Unanswered Questions Site Limitations Unclear Benefits to Producers Accountability. Before planting or harvest. After planting. After harvest. 1. Unanswered Questions.

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Limits

Limits. How fast and how far?. Limits. P hysical limitations The physics of the real world impose constraints on speed. L imits imposed by algorithm performance The intrinsic nature of certain problems presents limitations on what can be computed. A lgorithm computability

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Limits

Limits. By Erica Brackman. A Limit is…. The continuity of a function at a point of its domain The value the graph approaches at a certain point. Expressed with the notation: where a and L are numbers. Finding a Limit. Step 1: Simplify the function. Finding a Limit.

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Limits and Limits at infinity

Limits and Limits at infinity. Limit Review 1. Limits can be calculated 3 ways. Numerically Graphically Analytically (direct substitution) Properties of limits (pages 56-58). Graphically. Determine the value of y as x approaches some number c . Formal Definition of a Limit.

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Limits

Limits. y. y. y. Limit of a function. Improper limits. Limits “at” infinity. Show that. y. Worked example. Sometimes limits do not exist. x. x. x. x. definition of limit of a function. y. Notation. Vernacular

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Limits

Limits. Limits By: Table of Values Graph Piece-Wise Functions. Problem of the Day. Express the following sequences recursively: {-3, 1, 5, 9, ...} {4, 12, 36, 108, ...} Determine the sum of the following series. Label as either convergent or divergent at ∞ and give a reason.

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Rules for Capitalization

Rules for Capitalization. This is one of the easier parts of grammar. You already know most of them. 1. First word rule. Capitalize the first word of each sentence. (Was I right? Haven’t you known this one forever???) EX. Exceptional students always capitalize correctly.

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LIMITS

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LIMITS

LIMITS. Caleb Jacobson 11 th -12 th Grade Mathematics. Lim x as x goes to 5. C: 5. A: 0. D: 2. B : 10. Lim x^2+x-15 as x goes to 5. A: 25. C: 15. B: 30. D: 10. Lim (x-2)/x as x goes to 2. A: 0. C: 4. D: Undefined. B: 2. Lim 10/(x^3-15) as x goes to infinity. A: infinity.

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LIMITS

2. LIMITS. We have used calculators and graphs to guess the values of limits. However, we have learned that such methods don’t always lead to the correct answer. LIMITS. LIMITS. 2.3 Calculating Limits Using the Limit Laws. In this section, we will:

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LIMITS

LIMITS. If , find the following value of x in given table. What is Limits?. A limit is the maximum or minimum value that a given function. A limit will equal or approach (get closer to). Example:

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Limits

Limits. An Introduction To Limits Techniques for Calculating Limits One-Sided Limits; Limits Involving Infinity. Limit of a Function. The function is not defined at x = 2, so its graph has a “hole” at x = 2. Limit of a Function.

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Limits

Limits. Continuity. What happens at x = 2? What is f (2)? What happens near x = 2? f ( x ) is near - 3 What happens as x approaches 2? f ( x ) approaches - 3. Asymptotes. What happens at x = 1? What happens near x = 1?

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Limits

Limits. Calculus 2.1b part 2 of 2. 9/13/2012 – Today’s Learning Objective: Differentiability and Continuity. Find the derivative with respect to t for the function y = 2/ t. Differentiability and Continuity.

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Limits

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Limits

Limits. Why limits? What are limits? Types of Limits Where Limits Fail to Exist Limits Numerically and Graphically Properties of Limits Limits Algebraically Trigonometric Limits Average and Instantaneous Rates of Change Sandwich Theorem Formal Definition of a Limit. Why limits?.

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Rules for Brainstorming

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LIMITS

LIMITS. Chris Floyd Zach Hilley Aaron Hevenstone. LIMITS. A LIMIT IS THE VALUE A FUNCTION APPROACHES AT A CERTAIN POINT. Is it continuous?. Functions can have continuities, discontinuities, or even bothinuities.

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Rules for Indices

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