Find the limit (if it exists). $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( x + 5 ) ^ { 2 } } - 8 \right]$
A)5
B)-8
C)-5
D)0
E)does not exist

Question

Find the limit (if it exists).  $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( x + 5 ) ^ { 2 } } - 8 \right]$ 
A)5
B)-8
C)-5
D)0
E)does not exist

Quizplus · Accepted Answer

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

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

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