Question

Evaluate $ \lim_{x \to 2} \frac{x^2 - 4}{x - 2} $.

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

For limits yielding \( \frac{0}{0} \), factorize or simplify the expression to cancel common terms, then evaluate the limit.

Answer 1

The Correct Option is C

Evaluate the limit: \[ \lim_{x \to 2} \frac{x^2 - 4}{x - 2} \] Since substituting \( x = 2 \) gives \( \frac{0}{0} \), factorize the numerator: \[ x^2 - 4 = (x - 2)(x + 2) \] \[ \frac{x^2 - 4}{x - 2} = \frac{(x - 2)(x + 2)}{x - 2} = x + 2 \quad (x \neq 2) \] Now take the limit: \[ \lim_{x \to 2} (x + 2) = 2 + 2 = 4 \] Thus, the value of the limit is: \[ \boxed{4} \]