(Section 2.1: An Introduction to Limits) 2.1.15 How do we generalize this approach? (Perhaps look at Example 11 now.)The "Ignore a" Theorem for Two-Sided Limits: Evaluating the two-sided limit limx±afx()even iffis not a rational function with ain its domainIf: fis a function that is defined by the function rule rxon (i.e., throughout) some open x-interval containing the real constant a, possibly excluding a, itself, then: limx±a=limx±a, or neither limit exists. We can develop modified theorems for one-sided limits as follows. These modifications will be made clearer in Example 11. Basically, when evaluating a left-hand limit, we use the function rule that governs the x-values “immediately to the left” of aon the real number line. Likewise, when evaluating a right-hand limit, we use the
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