Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ .If the limiting value is infinite indicate whether it is +$\infty$ or -$\infty$. $f ( x ) = \frac { 4 - 2 x ^ { 3 } } { 6 x ^ { 3 } - 6 x + 1 }$
A)+$\infty$،-$\infty$
B)-$\infty$، +$\infty$
C) $- \frac { 1 } { 3 }$ , $- \frac { 1 } { 3 }$
D) $- \frac { 1 } { 3 }$ , $\frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

For both $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$, the highest degree term in both the numerator and denominator is $x^3$, so the limits simplify to the ratio of the coefficients of $x^3$ terms, which is $-\frac{2}{6} = -\frac{1}{3}$.

Find lim⁡x→+∞f(x)\lim _ { x \rightarrow + \infty } f ( x )limx→+∞​f(x)

Find $\lim _ { x \rightarrow + \infty } f ( x )$