CalcNotes0203-page16 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.16 PART H: “LONG-RUN” LIMITS FOR RATIONAL FUNCTIONS “Twin Limits” Property of Rational Functions If f is a rational function with its implied domain, then lim x ±² fx () = L (for some real constant L ) implies lim x ±²³ = L , and vice-versa. That is, if there is a “long-run” limit value L for as x “explodes” in one direction along the x -axis, then that value must also be the long-run limit value for as x explodes in the other direction. Therefore, the graph of f can have either no HAs or one HA, but not two. (See Examples 1, 3, and 11.) If f is not rational, then its graph could have zero, one, or two HAs. Example 13
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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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