Evaluate $$ \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi) $$ Enter the exact answer. $$ \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi)= $$ Number

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UpStudy AI · Accepted Answer

1. The limit is given by 
   $$
   \lim_{x \rightarrow 3\pi} \sin (x-3\pi)
   $$
   
2. Notice that as $$ x \rightarrow 3\pi $$, the expression $$ x-3\pi $$ approaches 0:
   $$
   \lim_{x \rightarrow 3\pi} (x-3\pi) = 0
   $$
   
3. Substitute this result into the sine function:
   $$
   \sin (x-3\pi) \rightarrow \sin(0)
   $$
   
4. Since $$\sin(0) = 0$$, we conclude that:
   $$
   \lim_{x \rightarrow 3\pi} \sin (x-3\pi) = 0
   $$
   
5. Therefore, the exact answer is $$0$$.
The limit is $$0$$.

Evaluate \( \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi) \) Enter the exact answer. \( \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi)= \) Number

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