CalcNotes0203-page15

CalcNotes0203-page15 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.15 Warning 2 : x 8 is the leading term because it is the term of higher degree, not because it is written first. In the long run, its impact renders the other term, ± x 6 , negligible by comparison. x 8 acts like a bully. It “explodes more dramatically” ± x 6 than does. Informal “Short Cut” Solution lim x ±² x 8 ³ x 6 () = lim x x 8 = ² A More Rigorous Solution: The Factoring Principle of Dominance We can factor out the dominant term, x 8 ( not the GCF), and we can apply the “Long-Run” Limit Rules for
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