Question

compute the limit and show your work. $lim_{x
ightarrow2}\frac{x^{2}-4}{x^{2}+4}$

Explanation:

Step1: Substitute x = 2

Substitute \(x = 2\) into the function \(\frac{x^{2}-4}{x^{2}+4}\).
\[

$$\begin{align*} \frac{2^{2}-4}{2^{2}+4}&=\frac{4 - 4}{4+4}\\ \end{align*}$$

\]

Step2: Simplify the expression

\[

$$\begin{align*} \frac{4 - 4}{4+4}&=\frac{0}{8}\\ &=0 \end{align*}$$

\]

Answer:

0