Question

find lim(x→∞) (-4x³ + 5x)/(2x³ + 7). choose 1 answer: a 5/7 b -2 c 0 d the limit is unbounded

Explanation:

Step1: Divide by highest - power of x in denominator

Divide both the numerator and denominator by $x^{3}$. We get $\lim_{x
ightarrow\infty}\frac{-4x^{3}/x^{3}+5x/x^{3}}{2x^{3}/x^{3}+7/x^{3}}=\lim_{x
ightarrow\infty}\frac{-4 + 5/x^{2}}{2+7/x^{3}}$.

Step2: Evaluate limits of individual terms

As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{5}{x^{2}} = 0$ and $\lim_{x
ightarrow\infty}\frac{7}{x^{3}}=0$. So, $\lim_{x
ightarrow\infty}\frac{-4 + 5/x^{2}}{2+7/x^{3}}=\frac{-4 + 0}{2+0}$.

Step3: Simplify the result

$\frac{-4+0}{2 + 0}=-2$.

Answer:

B. $-2$