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

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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).

Answer

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).

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

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