Find the limit and determine if the function is continuous at the point being approached.
-$$\lim _ { x \rightarrow 1 } \cos \left( \frac { 2 \pi } { 3 } \ln \left( e ^ { x } \right) \right)$$
A) $- \frac { 1 } { 2 }$; no
B) does not exist; no
C) 1; yes
D) $- \frac { 1 } { 2 } ;$ yes

Question

Quizplus · Accepted Answer

The limit can be found by substituting $x = 1$ into the function, which simplifies to $\cos\left(\frac{2\pi}{3}\ln(e)\right) = \cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}$. Since we can directly substitute $x = 1$ into the function without encountering any undefined expressions, the function is continuous at $x = 1$.

Find the Limit and Determine If the Function Is Continuous lim⁡x→1cos⁡(2π3ln⁡(ex))\lim _ { x \rightarrow 1 } \cos \left( \frac { 2 \pi } { 3 } \ln \left( e ^ { x } \right) \right)x→1lim​cos(32π​ln(ex))

Find the Limit and Determine If the Function Is Continuous $\lim _ { x \rightarrow 1 } \cos \left( \frac { 2 \pi } { 3 } \ln \left( e ^ { x } \right) \right)$