Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.1 Finding Limits Using Tables and Graphs - 13.1 Assess Your Understanding - Page 896: 38

The limit does not exist.

As we can see from the attached graph (the green one), as $x$ gets closer and closer to $2$ from the left, the value of the function (the $y$-value) gets closer and closer to $4$. But, as $x$ gets closer and closer to $2$ from the right, the value of the function (the $y$-value) gets closer and closer to $3$. Thus the limits from the two sides differ, therefore the limit does not exist.