For $f(x) = x + \frac{\lvert x - 1 \rvert}{x - 1}$, what is the right-hand limit at $x = 1$?

Explanation

1. 01

   For $x > 1$, $\lvert x - 1 \rvert = x - 1$, so $\frac{\lvert x - 1 \rvert}{x - 1} = 1$.

2. 02

   So $f(x) = x + 1 \to 2$ as $x \to 1^{+}$.