Unformatted text preview: x f x L →∞ = . Theorem: If r > 0 is a rational number, then 1 lim r x x →∞ = . If r > 0 is a rational number such that x r is defined for all x , then 1 lim r x x →∞ = . In General: • If a function f(x) approaches a certain number L as x gets larger and larger (or smaller and smaller), then f(x) has a horizontal asymptote at y = L . • A function can have zero, one or two horizontal asymptotes. • The graph of f(x) may intersect a horizontal asymptote, but never a vertical asymptote. Try Exercises 2, 4, 6, 13, 20, 22, 30, 40, 48 on pages 140142 in the textbook....
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 Spring '11
 Teague
 Calculus, Asymptotes, Limits, lim, Limit of a function, Asymptotic curve

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