2_6 - Section 2.6: Limits at Infinity & Horizontal...

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Unformatted text preview: 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 limx→∞ 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 limx→−∞ 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 limx→∞ f (x) = L or limx→−∞ f (x) = L Example 1 of Section 2.6 (textbook): Remarks: • Vertical Asymptote x = a ⇔ limx→a± f (x) = ±∞ (Infinite Limits) • Horizontal Asymptote y = L ⇔ limx→±∞ f (x) = L (Limits at Infinity) Example 3 of Section 2.6 (textbook): Example 4 of Section 2.6 (textbook): Example 5 of Section 2.6 (textbook): Example 6 of Section 2.6 (textbook): Example 7 of Section 2.6 (textbook): Definition of Infinite Limits at Infinity limx→±∞ f (x) = ±∞ means that, as x approaches (positive/ negative) infinity, the values of f (x) become arbitrarily large positive or negative. Example 8 of Section 2.6 (textbook): Example 9 of Section 2.6 (textbook): Example 10 of Section 2.6 (textbook): 1 ...
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

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