Find $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 5 + x ) ^ { 2 } } + 8 \right]$ (if it exists).
A) $\frac { 9 } { 25 }$
B) $- 8$
C) 8
D) $\infty$
E) limit does not exist

Question

Quizplus · Accepted Answer

As $x$ approaches $-\infty$, the term $\frac{x}{(5+x)^2}$ approaches 0 because the numerator grows linearly while the denominator grows quadratically. Therefore, the limit simplifies to $8$.

Find lim⁡x→−∞[x(5+x)2+8]\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 5 + x ) ^ { 2 } } + 8 \right]limx→−∞​[(5+x)2x​+8]

Find $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 5 + x ) ^ { 2 } } + 8 \right]$