CalcNotes0203-page12

CalcNotes0203-page12 - x < ; otherwise, lim x c...

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(Section 2.3: Limits and Infinity I) 2.3.12 PART F : "LONG - RUN" LIMIT RULES FOR c x k In Example 1, we saw that: lim x ±² 1 x = 0 , and lim x ±²³ 1 x = 0 . In Examples 6 and 7, we saw that: lim x ±² 1 x 1/3 = 0 , and lim x ±²³ 1 x 1/3 = 0 . In the graphs in Example 8, we see that: lim x ±² 1 x 1/2 = 0 , but lim x ±²³ 1 x 1/2 does not exist (DNE). Warning 1 : Be aware of this issue! More generally: If c is a real constant, and k is a positive rational constant, then: lim x ±² c x k = 0 . Also, lim x ±²³ c x k = 0 if x k is defined as a real quantity whenever
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Unformatted text preview: x < ; otherwise, lim x c x k does not exist (DNE). (See Footnote 4 for the justification. See also Footnote 5.) Think About It : What if k < ? Example 9 lim x 2 x 3 = , and lim x 2 x 3 = . Example 10 lim x x 3/4 = , but lim x x 3/4 , also written as lim x x 4 ( ) 3 , does not exist (DNE)....
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