Precalc0105to0107-pa - (Section 1.5 Piecewise-Defined Functions Limits and Continuity in Calculus 1.5.11 PART G CONTINUITY IN CALCULUS f is

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(Section 1.5: Piecewise-Defined Functions; Limits and Continuity in Calculus) 1.5.11 PART G: CONTINUITY IN CALCULUS f is continuous at a , or x = a ± 1) fa () is defined, 2) lim x ± a fx exists, and 3) lim x ± a = . f is discontinuous at a ± f is not continuous at a . (Some sources require that f be defined “around” a .) Comments 1) ensures that there is literally a point at a . 2) constrains the behavior of f immediately around a . 3) then ensures safe passage through the point
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This document was uploaded on 12/29/2011.

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