## Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

$$\lim _{x \rightarrow 2 } \frac{x^{2}-4}{x-2}=4$$
Given $$\lim _{x \rightarrow 2} \frac{x^{2}-4}{x-2}$$ Since from the following table \begin{array}{|c|c|c|c|c|c|}\hline x\to2^- & {1.9} & {1.99} & {1.999} & {1.9999} \\ \hline \frac{x^{2}-4}{ x-2} & {3.9} & {3.99} & {3.999} & {3.9999} \\ \hline\end{array} This means that $$\lim _{x \rightarrow 2^-} \frac{x^{2}-4}{x-2}=4$$and \begin{array}{|c|c|c|c|c|}\hline x \to2^+& {2.1} & {2.01} & {2.001} & {2.0001} \\ \hline \frac{x^{2}-4 }{ x-2} & {4.1} & {4.01} & {4.001} & {4.0001} \\ \hline\end{array} This means that $$\lim _{x \rightarrow 2^+} \frac{x^{2}-4}{x-2}=4$$ Hence, this means that $$\lim _{x \rightarrow 2 } \frac{x^{2}-4}{x-2}=4$$