One-sided Limits The expressions lim f(x) = L and lim, f(x) = L are called the one-sided limits of f (x) at a. x-a x-at Infinite Limits Consider the graph of the following rational functions and find the value of the limit of f(x) as x approaches to one. Definition of Infinite Limits Let f be a function defined on both sides of a, except possibly at a itself. Then lim f (x) = 00 and read "the limit of f (x), as x approaches a, is infinity" x-a x-a lim f (x) = -co and read "the limit of f (x), as x approaches a, is negative infinity" Definition of Vertical Asymptote The line x = a is called a vertical asymptote of the curve y = f (x) if at least one of the following x-a' statements is true: lim f (x) = co, lim f (x) = co, lim, f (x) = co, lim f (x) = -co, lim f (x) = -co, x -a- lim f(x) = -0o. -at