CalcNotes0203-page4

CalcNotes0203-page4 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.4 Example 3 (A Graph with No HAs) Let fx () = x + 3 . (Figure 2.3.c) We can write: lim x ±² = ² . This is because, as x increases without bound, the function values also (generally) increase without bound. Note : The use of “ = ” here may be technically inappropriate, but it is commonly accepted. Similarly, lim x ±²³ = ²³ . This is because, as x decreases without bound, the function values also (generally) decrease without bound. Because neither long-run limit exists, the graph has no HAs. Example 4 (Another Way for a Long-Run Limit to Not Exist)
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