AP Calculus AB Exam Question:

Find the limit algebraically:

lim(x->2) [(x^2 - 4) / (x - 2)]

Step-by-step solution:

To find the limit algebraically, we'll simplify the expression by factoring:

(x^2 - 4) can be factored as (x + 2)(x - 2).

Now we have:

lim(x->2) [(x^2 - 4) / (x - 2)] = lim(x->2) [(x + 2)(x - 2) / (x - 2)]

We can cancel out the common factor of (x - 2):

lim(x->2) [(x + 2)(x - 2) / (x - 2)] = lim(x->2) (x + 2)

Now we can plug in the limit value, x = 2, into the expression:

lim(x->2) (x + 2) = 2 + 2

= 4

Therefore, the limit of [(x^2 - 4) / (x - 2)] as x approaches 2 is equal to 4.