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