Find the following limit. \[ \lim _{x \rightarrow 0^{+}}(2 x \cot (\pi-x)) \]

Step 1 ：The given limit is \(\lim _{x \rightarrow 0^{+}}(2 x \cot (\pi-x))\).

Step 2 ：As x approaches 0 from the right, the limit is of the form 0/0. Therefore, we can use L'Hopital's rule to solve this limit.

Step 3 ：L'Hopital's rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

Step 4 ：We need to find the derivative of the numerator and the denominator. The derivative of 2x is 2. The derivative of cot(x) is -csc^2(x), and the derivative of π-x is -1. Therefore, the derivative of cot(π-x) is csc^2(π-x).

Step 5 ：After finding the derivatives, we substitute them back into the limit and solve.

Step 6 ：The limit of the function as x approaches 0 from the right is 0.

Step 7 ：Final Answer: The limit is \(\boxed{0}\).