Which of the following equal to limit $\lim _ { x \rightarrow 1 } \ln \left( \frac { x ^ { 4 } } { e ^ { 4 x } } \right)$ ?

A)-4
B)-1
C)1
D)4
E)Does not exist

Question

Which of the following equal to limit $\lim _ { x \rightarrow 1 } \ln \left( \frac { x ^ { 4 } } { e ^ { 4 x } } \right)$ ?

A)-4
B)-1
C)1
D)4
E)Does not exist

Quizplus · Accepted Answer

The limit can be simplified by applying properties of logarithms and limits. Specifically, $\lim _ { x \rightarrow 1 } \ln \left( \frac { x ^ { 4 } } { e ^ { 4 x } } \right)$ simplifies to $\ln \left( \frac { 1 ^ { 4 } } { e ^ { 4 \cdot 1 } } \right) = \ln \left( \frac { 1 } { e ^ { 4 } } \right) = \ln (1) - \ln (e^4) = 0 - 4 = -4$.

Which of the Following Equal to Limit lim⁡x→1ln⁡(x4e4x)\lim _ { x \rightarrow 1 } \ln \left( \frac { x ^ { 4 } } { e ^ { 4 x } } \right)limx→1​ln(e4xx4​)

Which of the Following Equal to Limit $\lim _ { x \rightarrow 1 } \ln \left( \frac { x ^ { 4 } } { e ^ { 4 x } } \right)$