Section 4.5 - Chapter Two: Limits Section 4.5: Limits at...

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Chapter Two: Limits Section 4.5: Limits at Infinity Just as vertical asymptotes were defined by Infinite Limits, we now define horizontal asymptotes in terms of Limits at Infinity. Formal Definition : Limit at Infinity Let L be a real number. 1. ( ) lim x f x L →∞ = means that for each 0 ε > there exists an M>0 such that ( ) x M f x L > - < . 2. ( ) lim x f x L →-∞ = means that for each 0 > there exists an N>0 such that ( ) x N f x L < - < . Limits at infinity are used to determine End Behavior: What happens at the very right ( ) ( ) x lim f x →∞ and very left ( ) ( ) x lim f x →-∞ of the function? Definition : Horizontal Asymptote The line y = L is a horizontal asymptote of the graph of f iff ( ) ( ) lim or lim x x f x L f x L →∞ →-∞ = = . Whenever the limit at (positive of negative) infinity is a real number, you automatically have a horizontal asymptote. To find a horizontal asymptote:
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This note was uploaded on 06/21/2011 for the course MTH 150 taught by Professor Marioborha during the Summer '11 term at Moraine Valley Community College.

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Section 4.5 - Chapter Two: Limits Section 4.5: Limits at...

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