find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise…

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise exist, enter dn\n$$lim _ { r \rightarrow infty } \frac { r - r ^ { 3 } } { 4 - r ^ { 2 } + 8 r ^ { 3 } }$$\nresources\nread it

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise exist, enter dn\n$$lim _ { r \rightarrow infty } \frac { r - r ^ { 3 } } { 4 - r ^ { 2 } + 8 r ^ { 3 } }$$\nresources\nread it

Answer

Explanation:

Step1: Divide numerator and denominator by (r^{3})

$$\lim_{r\rightarrow\infty}\frac{\frac{r}{r^{3}}-\frac{r^{3}}{r^{3}}}{\frac{4}{r^{3}}-\frac{r^{2}}{r^{3}}+\frac{8r^{3}}{r^{3}}}=\lim_{r\rightarrow\infty}\frac{\frac{1}{r^{2}} - 1}{\frac{4}{r^{3}}-\frac{1}{r}+8}$$

Step2: Apply the limit

As (r\rightarrow\infty), (\lim_{r\rightarrow\infty}\frac{1}{r^{2}} = 0), (\lim_{r\rightarrow\infty}\frac{4}{r^{3}}=0), (\lim_{r\rightarrow\infty}\frac{1}{r}=0) $$\frac{0 - 1}{0-0 + 8}=-\frac{1}{8}$$

Answer:

(-\frac{1}{8})