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2_6 - Section 2.6 Limits at Innity Horizontal Asymptotes...

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Section 2.6: Limits at Infinity & Horizontal Asymptotes Instructor: Ms. Hoa Nguyen ([email protected]) Definition of Limits at Infinity Let f be a function defined on some interval ( a, ). Then lim x →∞ f ( x ) = L means that, as x approaches positive infinity, the values of f ( x ) become arbitrarily close to L . Let f be a function defined on some interval ( -∞ , a ). Then lim x →-∞ f ( x ) = L means that, as x approaches negative infinity, the values of f ( x ) become arbitrarily close to L . Definition of Horizontal Asymptotes The line y = L is called a horizontal asymptote of f ( x ) if lim x →∞ f ( x ) = L or lim x →-∞ f ( x ) = L Example 1 of Section 2.6 (textbook): Remarks : Vertical Asymptote x = a lim x a ± f ( x ) = ±∞ (Infinite Limits)
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