Problem

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

Solution

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: \(4(2 + 2) = 16\).

From Solvely APP
Source: https://solvelyapp.com/problems/T8ScZ3k5nm/

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