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Unformatted text preview: stays nonnegative” as x ± ² , in the sense that x 10 ± 5 ² on the xinterval c , ± ( ) for some real constant c . Therefore, the radical “eventually” yields real values as x ± ² . In the radicand, x 10 ± 5 , x 10 dominates ± 5 . In the powerbase, x + 3 , x dominates 3. “Short Cut” Solution lim x ±² 4 x 3 ³ x 10 ³ 5 x + 3 ( ) 2 = lim x ±² 4 x 3 ³ x 10 x ( ) 2 = lim x ±² 4 x 3 ³ x 5 x 2 = lim x ±² ³ x 5 x 2 = lim x ±² ³ x 3 = ³ ² The Factoring Principle of Dominance should not be applied locally to the radicand, x 10 ± 5 . Example 20 will show how that approach can fail....
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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.
 Fall '10
 sturst
 Algebra, Limits

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