$f(x) = \frac{\log(1 + 2x)}{x}$ for $x \ne 0$, and $f(0) = k$. For which $k$ is $f$ continuous at $x = 0$?

Explanation

1. 01

   $\frac{\log(1 + 2x)}{x} = 2 \cdot \frac{\log(1 + 2x)}{2x}$.

2. 02

   $\frac{\log(1 + t)}{t} \to 1$, so the limit is 2.