1. (14 points) Consider the following function:
$$ f(x) = \begin{cases} 3x - 1, & x < 1; \\ 2x, & x \geq 1. \end{cases} $$
Use the $ \epsilon $-$\delta $ definition of the limit to show that $ \lim_{x \to 1} f(x) = 2 $. | | | | | |