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Limits at Infinity

Limits at Infinity - denominator then the limit of the...

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Limits at Infinity Limits at Infinity Section 3.5
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This section discusses the “end behavior” of a function on an interval. 3 ) ( lim = x f x
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Defn. of Horizontal Asymptote Defn. of Horizontal Asymptote The line y = L is a horizontal asymptote of the graph of f if or L x f x = -∞ ) ( lim L x f x = ) ( lim
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Thm. 3.10 Limits at Infinity Thm. 3.10 Limits at Infinity If r is a positive rational number and c is any real number, then Furthermore, if x is defined when x < 0, then 0 lim = r x x c 0 lim = -∞ r x x c
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Guidelines for Finding the Limits of Guidelines for Finding the Limits of Rational Functions Rational Functions If degree of numerator < degree of denominator then the limit of the rational function is 0. If degree of numerator = degree of
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Unformatted text preview: denominator, then the limit of the rational function is the ratio of the leading coefficients. If degree of numerator > degree of denominator, then the limit does not exist. Rational functions approach the same horizontal asymptote to the right and to the left. Functions that are not rational, however, may approach different horizontal asymptotes to the right and to the left. (Ex. 4 pg. 191) Show squeeze thm. Pg. 192 Ex. 5b. sin lim = ∞ → x x x 1 sin lim = → x x x cos 1 lim =-→ x x x Joke Time Joke Time What do you call the occupied restroom on an airplane? hy-pot-en-use What does a dentist scrape from your teeth? calculus...
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