CalcNotes0201-page16 - (Section 2.1 An Introduction to...

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(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 lim x ± a fx () even if f is not a rational function with a in its domain If: f is a function that is defined by the function rule rx on (i.e., throughout) some open x -interval containing the real constant a , possibly excluding a , itself, then: lim x ± a = lim x ± 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 a on the real number line. Likewise, when evaluating a right-hand limit, we use the
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