$$lim_{x\rightarrowinfty}(x^{2}-4)$$

Explanation:

Step1: Analyze the function behavior

As $x$ approaches $\infty$, the term $x^{2}$ dominates.

Step2: Determine the limit

Since $\lim_{x\rightarrow\infty}x^{2}=\infty$ and $\lim_{x\rightarrow\infty}(- 4)=-4$, then $\lim_{x\rightarrow\infty}(x^{2}-4)=\lim_{x\rightarrow\infty}x^{2}+\lim_{x\rightarrow\infty}(-4)=\infty$.

Answer:

$\infty$