: ANOTHER EXAMPLE 8 Prove that the limit does not exist. lim SOLUTION lim er - 1 - lim r- 1 = lim 1 : X lim - 1 1-I 11 lim = lim -1 -X 141-x-1 1+1-x - 1 z+1- Since the right- and left-hand limits are different, it follows from Video Example () Theorem 1 that the limit does not exist. The graph of the function f(x) = | x - 1 | / (x - 1) to the left supports the one-sided limits that we found. Need Help? Read It Submit