(Section 2.4: Limits and Infinity II) 2.4.2 Similarly, limx±0²fx()=²³. In words: “the limit of as xapproaches 0 from the left is negative infinity.” That is, as xapproaches 0 from lesser numbers, the function values (generally) decrease without bound. Therefore, limx±0does not exist (DNE), not even as ±or ±². (See Footnote 1.) As a consequence of limx±0+=²or limx±0²=(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) ±( limx±a+=²or³², or
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