Question:

Evaluate the limit below.

\lim_{{x \to 2}} \frac{{x^2 - 4}}{{x - 2}}

Answer:

To evaluate the limit, we cannot simply substitute $x = 2$ into the expression, as it would result in an indeterminate form of $\frac{0}{0}$.

To simplify the expression, we can factor the numerator:

\lim_{{x \to 2}} \frac{{(x - 2)(x + 2)}}{{x - 2}}

Next, we cancel out the common factor $(x - 2)$ in the numerator and denominator:

\lim_{{x \to 2}} (x + 2)

Now, we can substitute $x = 2$ into the expression:

\lim_{{x \to 2}} (2 + 2)

This simplifies to:

\lim_{{x \to 2}} 4

The limit evaluates to 4.

Therefore, the final answer is:

\lim_{{x \to 2}} \frac{{x^2 - 4}}{{x - 2}} = 4