2. -/1 points details my notes scalc9 6.8.008. find the limit. use lhospitals rule where appropriate. if…

2. -/1 points details my notes scalc9 6.8.008. find the limit. use lhospitals rule where appropriate. if there is a more elementary method, consider using it. lim(x→2) (x - 2)/(x² - 4)

2. -/1 points details my notes scalc9 6.8.008. find the limit. use lhospitals rule where appropriate. if there is a more elementary method, consider using it. lim(x→2) (x - 2)/(x² - 4)

Answer

Explanation:

Step1: Factor the denominator

We know that $x^{2}-4=(x + 2)(x - 2)$. So the function becomes $\lim_{x\rightarrow2}\frac{x - 2}{(x + 2)(x - 2)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 2)$ in the numerator and denominator. We get $\lim_{x\rightarrow2}\frac{1}{x + 2}$.

Step3: Substitute the value of $x$

Substitute $x = 2$ into $\frac{1}{x+2}$. So $\frac{1}{2 + 2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$