what is the limit? lim x→−2 x² - 4 / x + 2 dne -4 0 4

Explanation:

Step1: Factor the numerator

We know that $x^{2}-4=(x + 2)(x - 2)$. So the limit becomes $\lim_{x\rightarrow - 2}\frac{(x + 2)(x - 2)}{x+2}$.

Step2: Cancel out the common factor

Cancel out the $(x + 2)$ terms in the numerator and denominator. We get $\lim_{x\rightarrow - 2}(x - 2)$.

Step3: Substitute the value of x

Substitute $x=-2$ into $x - 2$. So $(-2)-2=-4$.

Answer:

B. -4