ABADEMCS SUPRORT \[ \begin{array}{l}\text { Use the Squeeze Theorem to find } \lim _{x \rightarrow 4} f(x) \text {, given that } 7-|x-4| \leq f(x) \leq 7+|x-4| \\ \lim _{x \rightarrow 4} f(x)=\text { Number }\end{array} \]

To apply the Squeeze Theorem, we first evaluate the two functions that bound \( f(x) \). 1. As \( x \) approaches 4, we analyze the bounds: - The lower bound is \( 7 - |x - 4| \). When \( x = 4 \), this evaluates to \( 7 - 0 = 7 \). As \( x \) approaches 4, \( |x - 4| \) approaches 0, so \( 7 - |x - 4| \) approaches 7. - The upper bound is \( 7 + |x - 4| \). Similarly, as \( x \) approaches 4, this becomes \( 7 + 0 = 7\). 2. Thus, we have \( 7 - |x - 4| \leq f(x) \leq 7 + |x - 4| \), both converging to 7 as \( x \) approaches 4. By the Squeeze Theorem: \[ \lim_{x \rightarrow 4} f(x) = 7. \] So, the answer is \( \lim_{x \rightarrow 4} f(x) = 7 \).