Question

find lim_x→∞ $\frac{-5x^{4}+2x}{x^{3}}$.
choose 1 answer:
a 2
b 0
c -5
d the limit is unbounded

Explanation:

Step1: Divide each term by $x^3$

$\lim_{x
ightarrow\infty}\frac{-5x^{4}+2x}{x^{3}}=\lim_{x
ightarrow\infty}(-5x+\frac{2}{x^{2}})$

Step2: Evaluate the limit of each term

As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{2}{x^{2}} = 0$ and $\lim_{x
ightarrow\infty}(-5x)=-\infty$. So the overall limit is unbounded.

Answer:

D. The limit is unbounded