Evaluate the limit: \( \lim_{x \to 2} \frac{4x^2 - 16}{x-2} \).

Step 1 ：First, we apply the limit to the function: \( \lim_{x \to 2} \frac{4x^2 - 16}{x-2} \).

Step 2 ：We try to substitute \(x = 2\) directly into the function, but this gives us \(\frac{0}{0}\), which is undefined. So, we must simplify the function before applying the limit.

Step 3 ：Next, we factor the numerator: \( \lim_{x \to 2} \frac{4(x - 2)(x + 2)}{x-2} \).

Step 4 ：The terms \((x-2)\) cancel out, leaving us with: \( \lim_{x \to 2} 4(x + 2) \).

Step 5 ：Now we can substitute \(x = 2\) directly into the function, resulting in: \(4(2 + 2) = 16\).