Hi all. I encountered the following problem: lim x->0 x * cot(x). My calculator gives the value of 1 for this limit, which can be corroborated by looking at the graph of y = x * cot(x). However, I reason that it should be zero, because: lim x->0 x * cot(x) = (lim x->0 x) * (lim x->0 cot(x)) = 0 * lim x->0 cot(x) = 0 (because anything multiplied by zero is zero.) Clearly, my reasoning is flawed. What is wrong with it? And what is the correct way to do this problem? Thank you.