CalcNotes0203-page24

CalcNotes0203-page24 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.24 Case 3 If deg N () > deg D , then the graph of f has no HAs. In particular, lim x ±² fx = ² or ³² , and lim x ±²³ = ³ or ²³ . If deg N = deg D + 1 , then the graph does have a slant asymptote (SA), also known as an oblique asymptote. See Example 15, where = ± 5 + 3 x 2 + 6 x 3 1 + 3 x 2 . (Think: Top heavy.) PART I: “LONG-RUN” LIMITS FOR ALGEBRAIC FUNCTIONS If we are considering a “long-run limit” as x , then we will say that, for rational constants a and b , x a dominates x b ± a > b . The same is true as x , provided that x a and x b are defined as real quantities whenever
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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