Question

limₓ→₂ \frac{4x - 8}{x² - 4} = \boxed{}

Explanation:

Step1: Factor numerator and denominator

Factor \(4x - 8\) as \(4(x - 2)\), and factor \(x^2 - 4\) using the difference of squares: \(x^2 - 4=(x - 2)(x + 2)\). So the expression becomes \(\lim_{x
ightarrow2}\frac{4(x - 2)}{(x - 2)(x + 2)}\).

Step2: Cancel common factor

Cancel out the common factor \((x - 2)\) (since \(x
eq2\) when taking the limit, we can do this). The expression simplifies to \(\lim_{x
ightarrow2}\frac{4}{x + 2}\).

Step3: Substitute \(x = 2\)

Substitute \(x = 2\) into \(\frac{4}{x + 2}\), we get \(\frac{4}{2 + 2}=\frac{4}{4}=1\).

Answer:

\(1\)