Find the value of the limit $\lim _ { x \rightarrow \infty } \frac { ( \ln x ) ^ { 2 } } { x }$ .
A) $- \infty$
B) $- 1$

C)0
D) $\frac { 1 } { e }$
E)1
F) $e$
G) $e ^ { \frac { 1 } { e } }$
H) $\infty$

Question

Find the value of the limit $\lim _ { x \rightarrow \infty } \frac { ( \ln x ) ^ { 2 } } { x }$ .
A) $- \infty$
B) $- 1$

C)0
D) $\frac { 1 } { e }$
E)1
F) $e$ 
G) $e ^ { \frac { 1 } { e } }$
H) $\infty$

Quizplus · Accepted Answer

The limit evaluates to 0 because as $x$ approaches infinity, the numerator $(\ln x)^2$ grows much slower than the denominator $x$, causing the fraction to approach 0.

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Find the Value of the Limit $\lim _ { x \rightarrow \infty } \frac { ( \ln x ) ^ { 2 } } { x }$