James says that the solution to $\underset{x}{lim}[\frac{1}{x}(x+1)]$ is $0$ because as $x$ tends to infinity, $\frac{1}{x}$ tends to $0,$ and $0$ times any number is $0.$ Is he right? If not, explain what he got wrong and find the limit using both L'Hopital's Rule and a method from earlier in the semester