Question

determine the following limit.
lim(x→∞) (30x³ + 3x² - 3x)/(35x³ + x² + 4x + 1)
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. lim(x→∞) (30x³ + 3x² - 3x)/(35x³ + x² + 4x + 1) = (simplify your answer.)
b. the limit as x approaches ∞ does not exist and is neither ∞ nor -∞.

Explanation:

Step1: Divide by highest - power term

Divide numerator and denominator by $x^{3}$: $\lim_{x
ightarrow\infty}\frac{30 + \frac{3}{x}-\frac{3}{x^{2}}}{35+\frac{1}{x}+\frac{4}{x^{2}}+\frac{1}{x^{3}}}$

Step2: Evaluate limits of terms

As $x
ightarrow\infty$, $\frac{1}{x},\frac{1}{x^{2}},\frac{1}{x^{3}}
ightarrow0$. So we get $\frac{30 + 0 - 0}{35+0 + 0+0}$

Answer:

A. $\frac{6}{7}$