1. evaluate the limit: $lim_{x\rightarrow2}\frac{x^{2}-4}{x - 2}$
1. evaluate the limit: $lim_{x\rightarrow2}\frac{x^{2}-4}{x - 2}$
Answer
Explanation:
Step1: Factor the numerator
We know that $x^{2}-4=(x + 2)(x - 2)$. So the limit becomes $\lim_{x\rightarrow2}\frac{(x + 2)(x - 2)}{x - 2}$.
Step2: Simplify the expression
Since $x\neq2$ (we are taking the limit as $x$ approaches 2, not setting $x = 2$), we can cancel out the $(x - 2)$ terms. The expression simplifies to $\lim_{x\rightarrow2}(x + 2)$.
Step3: Substitute the value of $x$
Substitute $x = 2$ into $x+2$. We get $2+2$.
Answer:
$4$