CalcNotes0203-page22

CalcNotes0203-page22 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.22 “Zoom Out” Property of HAs and SAs If we keep expanding the scope of the window of a grapher, then a graph with a HA or a SA will generally look more and more like the HA or SA. Example 16 Analyze the “long-run” behavior of the graph of fx () = ± 4 x 7 + 12 x 6 + 5 x 4 ± 23 x 3 + 11 4 x 3 ± 5 . Solution By Dominant Term Substitution, we find that: lim x ±² = lim x ³ 4 x 7 4 x 3 = lim x ³ x 4 = ³² lim x ±²³ = lim x ² 4 x 7 4 x 3 = lim x ² x 4 = ²³ If we perform Long Division, we obtain: = ± x 4 + 3 x 3 ± 2 + 1 4 x 3 ± 5 . The graph of y = ± x 4 + 3 x 3 ± 2 is a nonlinear asymptote that the
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