Evaluate the limit ${\lim }_{x\to 2}\frac{x^2-4}{x-2}$.

Solution

1. Factor the numerator as $x^2-4=(x-2)(x+2)$.
2. Substitute the factored form into the limit: ${\lim }_{x\to 2}\frac{(x-2)(x+2)}{x-2}$.
3. Cancel the common term $(x-2)$ to get ${\lim }_{x\to 2}(x+2)$.
4. Evaluate the limit by direct substitution: $2 + 2 = 4$.
5. Hence the answer is (C).