(Section 1.5: Piecewise-Defined Functions; Limits and Continuity in Calculus) 1.5.11PART G: CONTINUITY IN CALCULUSfis continuousat a, or x=a±1) fa()is defined, 2) limx±afxexists, and 3) limx±a=. fis discontinuousat a±fis not continuous at a. (Some sources require thatfbe defined “around” a.) Comments1)ensures that there is literally a point at a. 2)constrains the behavior offimmediately around a. 3)then ensures safe passage through the point
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