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: 34

$\dfrac{1}{4}$

As we can see from the attached graph (please refer to the green curve), as $x$ gets closer and closer to $2$ from the left and the right, the value of the function (the $y$-value) gets closer and closer to $\frac{1}{4}$. Thus, the limit is $\frac{1}{4}$.