CalcNotes0203-page23 - (Section 2.3 Limits and Infinity I...

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(Section 2.3: Limits and Infinity I) 2.3.23 In summary: “Super Short Cuts” for Evaluating “Long-Run” Limits for Rational Functions, and for Finding HAs for their Graphs Assume fx () = Nx Dx on its implied domain, where and are polynomials, and is not the zero polynomial. Let deg N and deg D be their respective degrees. Case 1 If deg N < deg D , then f is a proper rational function , and the x -axis y = 0 is the only HA of its graph. lim x ±² = 0 , and lim x ±²³ = 0 . See Example 14, where = x 2 ±
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