Find the lim_x→2 (x2-4)/(x-2)

The given limit is:

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.

The numerator $x^2 - 4$ is a difference of squares, which can be factored as $(x - 2)(x + 2)$.

Substitute the factored numerator back into the limit expression:

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.

Now, substitute $x=2$ into the simplified expression:

The limit is $\textbf{4}$.