(Section 1.5: Piecewise-Defined Functions; Limits and Continuity in Calculus) 1.5.10 Example 8 (Finding Limits; Revisiting Examples 1 and 2)Let the functionfbe defined by: fx()=x2,±2²x<1x+1,1²x²2³´µWhile f1=1+1=2, the left-hand limitlimx±1²=1. • When evaluating this left-hand limit, we only care about values of xthat are closeto 1 and lessthan 1. The top rule, =x2, is the only rule that applies to those xvalues. Therefore, limx±1²=limx±1²x2, which we can compute by evaluating x2at 1: lim
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