a) \( \underset{x \rightarrow 1}{\lim }\left(\underset{x}{ }(\underset{x}{ })\right. \) if \( h(x)=\left\{\begin{array}{l}1, \cdot x>1 \\ 3, x \leq 1\end{array}\right. \)

To understand the limit as \( x \) approaches 1 for the function \( h(x) \), we first need to evaluate the two cases. If \( x > 1 \), \( h(x) = 1 \), and if \( x \leq 1 \), \( h(x) = 3 \). As \( x \) approaches 1 from the left (values less than 1), \( h(x) \) will consistently be equal to 3. From the right (values greater than 1), it will instantly jump to 1. Therefore, the limit does not approach a single value from both sides as it is discontinuous at that point. Thus, the limit does not exist as \( x \) approaches 1, because the left-hand limit is 3 and the right-hand limit is 1: \[ \underset{x \rightarrow 1}{\lim }h(x) \text{ does not exist}. \]