Question 8 \[ \lim _{x \rightarrow 0}\left(\csc 2 x-\frac{1}{2 x}\right)= \] 0 2 1 $-1$ None of these

Step 1 ：Define the function as \(f(x) = \csc(2x) - \frac{1}{2x}\)

Step 2 ：Find the derivative of the numerator, which is \(-2\cot(2x)\csc(2x) + \frac{1}{2x^2}\)

Step 3 ：Find the derivative of the denominator, which is 0

Step 4 ：Calculate the limit as x approaches 0 for the ratio of the derivative of the numerator to the derivative of the denominator

Step 5 ：The limit is of the form \(\frac{\infty}{0}\), which is undefined

Step 6 ：\(\boxed{\text{None of these}}\) is the final answer because the limit does not exist