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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.
 Fall '08
 Noohi
 Calculus, Asymptotes, Limits

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