Horizontal asymptote

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Definition

For a curve

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For a function

Suppose f is a function whose domain contains an interval of the form (a,\infty) for some real number a or an interval of the form (-\infty,b) for some real number b. We say that the line y = L is a horizontal asymptote for the graph of f if one or both of these holds:

\! \lim_{x \to \infty} f(x) = L, \qquad \lim_{x \to -\infty} f(x) = L

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