Why is the limit of $x \log x$ as $x$ tends to $0^+$, $0$?
- The limit of $x$ as $x$ tends to $0$ is $0$.
- The limit of $\log x$ as $x$ tends to $0^+$ is $-\infty$.
- The limit of products is the product of each limit, provided each limit exists.
- Therefore, the limit of $x \log x$ as $x$ tends to $0^+$ should be $0 \times (-\infty)$, which is undefined and not $0$.