Find $\lim _ { x \rightarrow + \infty } \left[ \frac { x } { ( 2 + x ) ^ { 2 } } - 2 \right]$ (if it exists).
A) $- \frac { 1 } { 2 }$
B)2
C)-2
D)$\infty$
E)does not exist

Question

Quizplus · Accepted Answer

To find the limit as $x$ approaches $+\infty$ for the given expression, we can simplify the expression and analyze its behavior as $x$ grows large. The expression is $\frac{x}{(2+x)^2} - 2$. As $x$ approaches infinity, the term $\frac{x}{(2+x)^2}$ approaches 0 because the denominator grows faster than the numerator. Therefore, the expression simplifies to $0 - 2 = -2$ as $x$ approaches infinity.

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

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