In(4x ) EXAMPLE 3 Calculate lim X - 0 4 x SOLUTION Since In(4x) - co and -> co as X > co, I'Hospital's Rule applies: In(4x) 1/X lim X - 00 4 x = lim 1x-3/4. X - 00 4" Notice that the limit on the right side is now indeterminate of type . But instead of applying l'Hospital's Rule a second time as we did in this example, we simplify the expression and see that a second application is unnecessary: In(4x) 1/X 4 lim = lim 1 -3/4 = lim X - 0 4 x X - 00 4' X - 0o /x