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Precalc0101to0102-page20

Precalc0101to0102-page20 - (Section 1.1 Functions 1.1.19 1...

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(Section 1.1: Functions) 1.1.19 3. Series expansions of [defining expressions of] functions. Let fx () = 1 1 ± x . In Section 9.4 and in calculus , you will see that has the infinite series expansion 1 + x + x 2 + x 3 + ..., provided that ± 1 < x < 1. In calculus , you will consider series expansions for sin x , cos x , e x , etc. 4. The Zero Factor Property and inequalities. • According to the Zero Factor Property, if ab = 0 for real numbers a and b , then a = 0 or b = 0 . • If we were solving the equation 2 tt + 10 = 0 , we could use the Zero Factor Property. 2 + 10 = 0 ± t = 0 or t = ² 10 ³ ´ µ • In Example 16, we essentially solved the inequality 2 + 10 ± 0 . ‘~’ denotes negation (“not”). 2 + 10 ± 0 ² ~ t = 0 or t = ³ 10 ´ µ · ² ~ t = 0 and ~ t = ³ 10 ´ µ · by DeMorgan's Laws of logic (see below) ² t ± 0 and t ±³ 10 ´ µ · • By DeMorgan’s Laws of logic, ~ p or q is logically equivalent to ~ p and ~ q ± ² ³ ´ . For example: If I am an American, then (I am an Alabaman) or (I am an Alaskan) or …. If I am not an American, then (I am not an Alabaman) and
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