Evaluate the limit lim x→2 (x^2 - 4)/(x - 2).

Evaluate the limit lim x→2 (x^2 - 4)/(x - 2).

Step 1: Identify the limit we want to evaluate: lim x→2 (x^2 - 4)/(x - 2).
Step 2: Substitute x = 2 into the expression. We get (2^2 - 4)/(2 - 2) = (4 - 4)/(0) = 0/0, which is an indeterminate form.
Step 3: Since we have an indeterminate form, we can use L'Hôpital's Rule. This rule states that if we have 0/0 or ∞/∞, we can take the derivative of the numerator and the derivative of the denominator.
Step 4: Find the derivative of the numerator (x^2 - 4). The derivative is 2x.
Step 5: Find the derivative of the denominator (x - 2). The derivative is 1.
Step 6: Now we can rewrite the limit using the derivatives: lim x→2 (2x)/(1).
Step 7: Substitute x = 2 into the new expression: (2*2)/(1) = 4/1 = 4.
Step 8: Therefore, the limit lim x→2 (x^2 - 4)/(x - 2) equals 4.

Limit Evaluation – Understanding how to evaluate limits, particularly when encountering indeterminate forms.
L'Hôpital's Rule – Application of L'Hôpital's Rule to resolve limits that result in indeterminate forms like 0/0.
Factoring – Recognizing that the expression can be simplified by factoring before applying limit techniques.