Evaluate the limit $\lim _ { x \rightarrow \infty } \frac { \ln \left( x ^ { 3 } \right) } { x ^ { 10 } }$ using L'Hopital's Rule if necessary.
A) $\frac { 10 } { 3 }$
B) $\infty$
C) $- \infty$
D) $\frac { 3 } { 10 }$
E) 0

Question

Evaluate the limit $\lim _ { x \rightarrow \infty } \frac { \ln \left( x ^ { 3 } \right) } { x ^ { 10 } }$ using L'Hopital's Rule if necessary. 
A) $\frac { 10 } { 3 }$
B) $\infty$
C) $- \infty$
D) $\frac { 3 } { 10 }$
E) 0

Quizplus · Accepted Answer

Applying L'Hopital's Rule, we get

$$\lim_{x \rightarrow \infty} \frac{\ln (x^3)}{x^{10}} = \lim_{x \rightarrow \infty} \frac{3 \ln x}{10x^9}$$

Applying L'Hopital's Rule again, we get

$$\lim_{x \rightarrow \infty} \frac{3 \ln x}{10x^9} = \lim_{x \rightarrow \infty} \frac{3}{10x^8} = 0$$

Therefore, the answer is E, 0.

Evaluate the Limit lim⁡x→∞ln⁡(x3)x10\lim _ { x \rightarrow \infty } \frac { \ln \left( x ^ { 3 } \right) } { x ^ { 10 } }limx→∞​x10ln(x3)​

Evaluate the Limit $\lim _ { x \rightarrow \infty } \frac { \ln \left( x ^ { 3 } \right) } { x ^ { 10 } }$