CalcNotes0204-page2

CalcNotes0204-page2 - (Section 2.4: Limits and Infinity II)...

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(Section 2.4: Limits and Infinity II) 2.4.2 Similarly, lim x ± 0 ² fx () = ²³ . In words: “the limit of as x approaches 0 from the left is negative infinity.” That is, as x approaches 0 from lesser numbers, the function values (generally) decrease without bound. Therefore, lim x ± 0 does not exist (DNE), not even as ± or ±² . (See Footnote 1.) As a consequence of lim x ± 0 + = ² or lim x ± 0 ² = (either alone would have been sufficient), the graph of x = 0 (i.e., the y -axis) is a vertical asymptote (VA) for the graph of y = . Using Infinite Limits at a Point to Find Vertical Asymptotes (VAs) The graph of y = has a vertical asymptote (VA) at x = a (for a real constant a ) ± ( lim x ± a + = ² or ³² , or
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