Find the lim_x→2 (x2-4)/(x-2)

Step 1: Identify the limit expression. The given limit is: $\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$

Step 2: Check for indeterminate form. If we substitute $x=2$ directly into the expression, we get $\frac{2^2 - 4}{2 - 2} = \frac{4 - 4}{0} = \frac{0}{0}$, which is an indeterminate form. This means we need to simplify the expression.

Step 3: Factor the numerator. The numerator $x^2 - 4$ is a difference of squares, which can be factored as $(x - 2)(x + 2)$. $x^2 - 4 = (x - 2)(x + 2)$

Step 4: Simplify the expression. Substitute the factored numerator back into the limit expression: $\lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2}$ Since $x \to 2$, $x$ is approaching 2 but is not equal to 2. Therefore, $x - 2 \neq 0$, and we can cancel out the $(x - 2)$ term from the numerator and denominator. $\lim_{x \to 2} (x + 2)$

Step 5: Evaluate the limit. Now, substitute $x=2$ into the simplified expression: $2 + 2 = 4$ The limit is $\boxed{4}$.

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