Question

Limit x tends to 0 (x cot 2x)

Answer 1

Explanation:

`= \lim \limits_(x \to0)x \cot(2x)`

`= \lim \limits_(x \to0) (x)/( \tan(2x) )`

`= \lim \limits_(x \to0) (x)/( \tan(2x) ) * (2x)/(2x)`

`= \lim \limits_(x \to0) (2x)/( \tan(2x) ) * \lim \limits_(x \to0) (x)/(2x)`

`= \lim \limits_(u \to0) (u)/( \tan(u) ) * (1)/(2)`

`= (1)/(2)`