1. The problem statement, all variables and given/known data A problem in my book asks the reader to evaluate lim x→0 xln(2x) using L'Hôpital. 2. Relevant equations None 3. The attempt at a solution I think I got it right but I simply wanted to make sure I did no illegal manipulations (I'm self-studying this stuff). I started by substituting u = 1/x to get an undeterminate form suitable for L'Hôpital. By doing so, lim x→0 becomes lim u→∞ lim x→0 xln(2x) = lim u→∞ ln(2/u) / u Applying L'Hôpital: = lim u→∞ (-u)/2u2 = lim u→∞ (-1)/2u = 0 I know that's the right answer, but did I make any mistakes? Also, was I allowed to switch lim x→0 by lim u→∞? Thanks in advance!