MATH 1171-*** 2.5 Infinite limits D4-x Definition 1. lim f(x) = means that the values of f(x) can be made arbitrarily large by taking x sufficiently close to a (on either side of a) but not equal to a. a lim f(x) = + xa a lim f(x) = +0 lim f(x)= xa+ Definition 2. The line x = a is a vertical asymptote of y = f(x) if lim f(x) = or lim f(x) = 0. a+ We only need him f(x) x xa or lim f(x) to be (+/-) infinite in order to xa+ -1/c Ex: f(x) = e at x=0 - have a VA at x = a. y=ex lim e x 0+ (as x 0+, lim xc OC = + (0500, +00) (as x x=0 is a VA. Domain: (-,0) U (0,) x=0 The candidates for VAs are the open endpoints in the domain of f.