Find the limit and determine if the function is continuous at the point being approached.
-$$\lim _ { x \rightarrow 2 \pi } \sin \left( \frac { 9 \pi } { 2 } \cos ( \tan x ) \right)$$
A) 1; no
B) does not exist; yes
C) does not exist; no
D) 1; yes

Question

Quizplus · Accepted Answer

As $ x \rightarrow 2\pi $, $\tan x \rightarrow 0$, so $\cos(\tan x) \rightarrow \cos(0) = 1$. Thus, $\frac{9\pi}{2} \cos(\tan x) \rightarrow \frac{9\pi}{2}$. Since $\sin\left(\frac{9\pi}{2}\right) = 1$, the limit is 1. The function is continuous at $x = 2\pi$ because $\sin$ and $\cos$ are continuous functions.

Find the Limit and Determine If the Function Is Continuous lim⁡x→2πsin⁡(9π2cos⁡(tan⁡x))\lim _ { x \rightarrow 2 \pi } \sin \left( \frac { 9 \pi } { 2 } \cos ( \tan x ) \right)x→2πlim​sin(29π​cos(tanx))

Find the Limit and Determine If the Function Is Continuous $\lim _ { x \rightarrow 2 \pi } \sin \left( \frac { 9 \pi } { 2 } \cos ( \tan x ) \right)$