Find $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 5 + x ) ^ { 2 } } + 7 \right]$ (if it exists).
A) $\frac { 8 } { 25 }$
B) $- 7$
C) 7
D) $\infty$
E) limit does not exist

Question

Quizplus · Accepted Answer

The given expression can be simplified by dividing each term in the numerator by the highest power of $x$ in the denominator, which is $x^2$. As $x$ approaches $-\infty$, the term $\frac{x}{(5+x)^2}$ approaches 0 because the degree of $x$ in the numerator is less than the degree of $x$ in the denominator. Therefore, the limit simplifies to $0 + 7 = 7$.

Find lim⁡x→−∞[x(5+x)2+7]\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 5 + x ) ^ { 2 } } + 7 \right]limx→−∞​[(5+x)2x​+7]

Find $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 5 + x ) ^ { 2 } } + 7 \right]$