(Section 1.1: Functions)1.1.19 3.Series expansions of [defining expressions of] functions. Let fx()=11±x. In Section 9.4 and in calculus, you will see that has the infinite series expansion1+x+x2+x3+..., provided that ±1<x<1. In calculus, you will consider series expansions for sinx, cosx, ex, etc. 4.The Zero Factor Property and inequalities. • According to the Zero Factor Property, if ab=0 for real numbers aand b, then a=0 or b=0 . • If we were solving the equation 2tt+10=0 , we could use the Zero Factor Property. 2+10=0±t=0or t=²10³´µ¶• In Example 16,we essentially solved the inequality 2+10±0 . ‘~’ denotes negation (“not”). 2+10±0²~t=0or t=³10´µ¶·²~t=0and ~t=³10´µ¶·by DeMorgan's Laws of logic (see below)²t±0and t±³10´µ¶·• By DeMorgan’s Laws of logic, ~por qis logically equivalent to ~pand ~q±²³´. For example: If I am an American, then (I am an Alabaman) or(I am an Alaskan) or…. If I am notan American, then (I am notan Alabaman) and
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