Here is an example in Wolfram Alpha. A student had been given the assignment of finding the limit as $n$ tends to infinity of $\frac{1}{1+\frac{(-1)^n}{log(n)}}$. He had correctly arrived at the answer 1. Now he used WA to check if he was correct. WA returned 0 (the command lim n-> inf 1/(1-(-1)^n/log(n)) ). On examining the steps, it turned out that WA had manipulated a bit and used L'Hopital on the expression $\frac{log(n)}{(-1)^n+log(n)}$.
Note that if one instead asks for the limit of $\frac{1}{1-\frac{(-1)^n}{log(n)}}$ WA correctly returns 1, using the same method one usually would.