Question

determine the following limit.
lim_{x
ightarrowinfty}\frac{20x^{3}+5x^{2}-5x}{8x^{3}+x^{2}+3x + 2}
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. lim_{x
ightarrowinfty}\frac{20x^{3}+5x^{2}-5x}{8x^{3}+x^{2}+3x + 2}=square (simplify your answer.)
b. the limit as x approaches (infty) does not exist and is neither (infty) nor (-infty).

Explanation:

Step1: Divide by highest - power term

Divide numerator and denominator by $x^{3}$: $\lim_{x
ightarrow\infty}\frac{20 + \frac{5}{x}-\frac{5}{x^{2}}}{8+\frac{1}{x}+\frac{3}{x^{2}}+\frac{2}{x^{3}}}$

Step2: Evaluate limits of individual terms

As $x
ightarrow\infty$, $\frac{1}{x},\frac{1}{x^{2}},\frac{1}{x^{3}}
ightarrow0$. So we get $\frac{20 + 0-0}{8 + 0+0+0}$

Answer:

$\frac{20}{8}=\frac{5}{2}$