find $lim_{x\rightarrowinfty}\frac{x^{2}-4}{x + 4}$. choose 1 answer: a 1 b -1 c 0 d the limit is unbounded

Explanation:

Step1: Divide numerator and denominator by x

Divide both $x^{2}-4$ and $x + 4$ by $x$. We get $\lim_{x\rightarrow\infty}\frac{x-\frac{4}{x}}{1+\frac{4}{x}}$.

Step2: Evaluate the limit of each term

As $x\rightarrow\infty$, $\lim_{x\rightarrow\infty}\frac{4}{x}=0$. So, $\lim_{x\rightarrow\infty}\frac{x-\frac{4}{x}}{1+\frac{4}{x}}=\lim_{x\rightarrow\infty}\frac{x - 0}{1+0}$.

Step3: Simplify the expression

$\lim_{x\rightarrow\infty}\frac{x}{1}=\infty$. So the limit is unbounded.

Answer:

D. The limit is unbounded