Questions: lim as x approaches π of sin(2x - sin(6x)) =

Transcript text: \[ \lim _{x \rightarrow \pi} \sin (2 x-\sin (6 x))= \]

Solution

Solution Steps

To evaluate the limit of the function as \( x \) approaches \(\pi\), we can directly substitute \( x = \pi \) into the function since it is continuous at this point. This will give us the value of the limit.

Step 1: Evaluate the Function at \( x = \pi \)

To find the limit of the function \( \lim_{x \rightarrow \pi} \sin(2x - \sin(6x)) \), we substitute \( x = \pi \) into the function. This is possible because the sine function is continuous everywhere.

Step 2: Substitute and Simplify

Substitute \( x = \pi \) into the function:

\[ \sin(2\pi - \sin(6\pi)) \]

Since \(\sin(6\pi) = 0\), the expression simplifies to:

\[ \sin(2\pi - 0) = \sin(2\pi) \]

Step 3: Evaluate \(\sin(2\pi)\)

The value of \(\sin(2\pi)\) is 0.