CalcNotes0202-page3

CalcNotes0202-page3 - h here to avoid confusion with the...

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(Section 2.2: Properties of Limits and Algebraic Functions) 2.2.3 These properties, together with the basic rules lim x ± a c = c and lim x ± a x = a for real constants a and c , justify our Limit Theorems for Rational Functions. Example 1 Evaluate lim x ± 4 3 x 2 ² 1 x + 5 . Solution 1 (Applying our Limit Theorems for Rational Functions) If hx () = 3 x 2 ± 1 x + 5 , then h is a rational function with implied domain x ± ± x ²³ 5 {} . We observe that 4 is in the domain of h , so we substitute (“plug in”) x = 4 and evaluate h 4 () . (We call the function
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Unformatted text preview: h here to avoid confusion with the use of f and g in the list of properties.) lim x ± 4 3 x 2 ² 1 x + 5 = 3 4 ( ) 2 ² 1 4 ( ) + 5 = 47 9 Solution 2 (The “Long Way”: Applying the Limit Properties) lim x ± 4 3 x 2 ² 1 x + 5 = lim x ± 4 3 x 2 ² 1 ( ) lim x ± 4 x + 5 ( ) = lim x ± 4 3 x 2 ² lim x ± 4 1 lim x ± 4 x + lim x ± 4 5 = lim x ± 4 3 x 2 ² 1 4 + 5 = 3 lim x ± 4 x 2 ( ) ² 1 4 + 5 = 3 lim x ± 4 x ( ) 2 ² 1 4 + 5...
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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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