AP Calculus AB Exam Question:

Evaluate the following limit:

Answer:

To evaluate the limit $\lim_{x \to 2} \frac{x^2 - 4}{x-2}$, we need to see what happens as $x$ approaches 2 from both the left and right sides.

Step 1:

First, let's substitute $x = 2$ directly into the expression:

We encounter an indeterminate form, since we have 0 in the denominator. Therefore, we need to utilize different techniques to evaluate the limit.

Step 2:

One way to proceed is to factor the numerator:

Step 3:

Now, we can cancel out the common factor of $(x-2)$:

Step 4:

Since there are no more indeterminate forms or discontinuities, we can evaluate the limit by simply substituting $x=2$ into the expression:

Therefore, $\lim_{x \to 2} \frac{x^2 - 4}{x-2} = 4$.