Read the two statements and choose the correct option.

I. If $\lim_{x \to a^{-}} f(x) = f(a)$, then $f$ is continuous at $x = a$.

II. If $f$ is continuous at $x = a$, then $\lim_{h \to 0} f(a + h) = f(a)$.

Explanation

1. 01

   I is false: $f(x) = x$ for $x \le 1$ and $x + 1$ for $x > 1$ has left limit $1 = f(1)$ but right limit 2.

2. 02

   II is true: $\lim_{h \to 0} f(a + h)$ is $\lim_{x \to a} f(x)$ written with $x = a + h$, and continuity makes it $f(a)$.