Lesson 4 One-sided limits and Squeeze Theorem 4

Lesson 4 One-sided limits and Squeeze Theorem 4 -...

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One-Sided Limits
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Objectives At the end of the discussion, the students, at the minimum, should be able to: - Discuss fully the concept of one-sided limits - Evaluate one-sided limits - Determine Vertical and horizontal asymptotes of functions - Evaluate limits of functions using the Squeeze Theorem
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Definition of One-Sided Limits
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DEFINITION : Vertical Asymptote -∞ = + ∞ = -∞ = + ∞ = - - + + ) x ( f lim . d ) x ( f lim . c ) x ( f lim . b ) x ( f lim . a a x a x a x a x The line is a vertical asymptote of the graph of the function if at least one of the following statement is true: x a = ( 29 y f x =
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x=a 0 x=a + ∞ = + ) x ( f lim a x + ∞ = - ) x ( f lim a x The following figures illustrate the vertical asymptote . x a = 0
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x=a 0 x=a -∞ = - ) x ( f lim a x -∞ = + ) x ( f lim a x The following figures illustrate the vertical asymptote . x a = 0
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DEFINITION : Horizontal Asymptote b ) x ( f lim or b ) x ( f lim x x = = -∞ + ∞ The line is a horizontal asymptote of the graph of the function if either b y = ( 29 y f x =
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This note was uploaded on 10/19/2011 for the course MATH 21 taught by Professor Ma'amrosarioexconde during the Summer '11 term at Mapúa Institute of Technology.

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Lesson 4 One-sided limits and Squeeze Theorem 4 -...

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